MathsGee Wits Club - Recent questions in MATH1042A (Engineering)
https://wits.mathsgee.com/questions/math1043a-engineering-maths
Thanks to Q2ASolve the linear equation:
https://wits.mathsgee.com/541/solve-the-linear-equation
Solve the equation:<br />
<br />
\(5(2-3x)+3(5x-2)-7(4-x)=0\)MATH1042A (Engineering)https://wits.mathsgee.com/541/solve-the-linear-equationThu, 02 Sep 2021 01:58:09 +0000What is the definition of arcsin?
https://wits.mathsgee.com/539/what-is-the-definition-of-arcsin
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/539/what-is-the-definition-of-arcsinThu, 02 Sep 2021 01:35:10 +0000What are the condition for the existence of an inverse trigonometric function?
https://wits.mathsgee.com/537/what-condition-existence-inverse-trigonometric-function
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/537/what-condition-existence-inverse-trigonometric-functionThu, 02 Sep 2021 01:32:56 +0000Given \(y=2 x=f(x)\) find \(f^{-1}\)
https://wits.mathsgee.com/536/given-y-2-x-f-x-find-f-1
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/536/given-y-2-x-f-x-find-f-1Thu, 02 Sep 2021 01:31:51 +0000What is the notation for inverse trigonometric functions?
https://wits.mathsgee.com/534/what-is-the-notation-for-inverse-trigonometric-functions
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/534/what-is-the-notation-for-inverse-trigonometric-functionsThu, 02 Sep 2021 01:30:18 +0000If two lines in the cartesian plane are perpendicular, show that the angles they make with the positive \(x\) axis can be written as \(\alpha\) and \(\frac{\pi}{2}+\alpha\) for some \(\alpha\).
https://wits.mathsgee.com/533/lines-cartesian-perpendicular-angles-positive-written-alpha
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/533/lines-cartesian-perpendicular-angles-positive-written-alphaThu, 02 Sep 2021 01:29:21 +0000Find all the solutions between 0 and \(2 \pi\) of the equations
https://wits.mathsgee.com/532/find-all-the-solutions-between-0-and-2-pi-of-the-equations
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/532/find-all-the-solutions-between-0-and-2-pi-of-the-equationsThu, 02 Sep 2021 01:28:21 +0000Find the general equation of the trigonometric equations using a calculator (in radian mode) to find the solutions to 4 decimal places.
https://wits.mathsgee.com/531/general-equation-trigonometric-equations-calculator-solutions
<p>Find the general equation of the trigonometric equations using a calculator (in radian mode) to find the solutions to 4 decimal places.</p>
<ol>
<li>\(3 \cos 3 x=1\)</li>
<li>\(\sin 3 \theta-\sin \theta=\frac{1}{2} \cos 2 \theta\)</li>
<li>\(3+5 \cos \theta+6 \cos 2 \theta=0\)</li>
</ol>MATH1042A (Engineering)https://wits.mathsgee.com/531/general-equation-trigonometric-equations-calculator-solutionsThu, 02 Sep 2021 01:27:29 +0000Find the general equation of the trigonometric equation \(\sin ^{2} 3 x-\sin ^{2} x=\sin ^{2} 2 x\)
https://wits.mathsgee.com/530/find-the-general-equation-the-trigonometric-equation-sin-sin
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/530/find-the-general-equation-the-trigonometric-equation-sin-sinThu, 02 Sep 2021 01:25:11 +0000Find the general equation of the trigonometric equation \(\sin 3 \theta-\sin \theta=\cos 2 \theta\)
https://wits.mathsgee.com/529/general-equation-trigonometric-equation-theta-theta-theta
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/529/general-equation-trigonometric-equation-theta-theta-thetaThu, 02 Sep 2021 01:24:15 +0000Find the general equation of the trigonometric equation \(\cos 3 x=\sin 2 x\)
https://wits.mathsgee.com/528/find-the-general-equation-the-trigonometric-equation-cos-sin
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/528/find-the-general-equation-the-trigonometric-equation-cos-sinThu, 02 Sep 2021 01:23:09 +0000Find the general equation of the trigonometric equation \[\cos 4 x=\sin 2 x\]
https://wits.mathsgee.com/527/find-the-general-equation-the-trigonometric-equation-cos-sin
<p>Find the general equation of the trigonometric equation</p>
<p>\[\cos 4 x=\sin 2 x\]</p>
<p><strong>Hint: \(\sin 2 x=\cos \left(\frac{\pi}{2}-2 x\right)\)</strong></p>MATH1042A (Engineering)https://wits.mathsgee.com/527/find-the-general-equation-the-trigonometric-equation-cos-sinThu, 02 Sep 2021 01:21:34 +0000Prove that \(\dfrac{\tan 3 A}{\tan A}=\dfrac{2 \cos 2 A+1}{2 \cos 2 A-1}\)
https://wits.mathsgee.com/526/prove-that-dfrac-tan-3-a-tan-a-dfrac-2-cos-2-a-1-2-cos-2-a-1
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/526/prove-that-dfrac-tan-3-a-tan-a-dfrac-2-cos-2-a-1-2-cos-2-a-1Thu, 02 Sep 2021 01:18:00 +0000Express \(\cos ^{4} \theta\) and \(\sin ^{4} \theta \cos ^{2} \theta\) in terms of cosines of multiples of \(\theta\)
https://wits.mathsgee.com/525/express-theta-theta-cos-theta-terms-cosines-multiples-theta
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/525/express-theta-theta-cos-theta-terms-cosines-multiples-thetaThu, 02 Sep 2021 01:17:16 +0000Prove that \(\cos 3 \theta=4 \cos ^{3} \theta-3 \cos \theta .\) (Hint: \(\left.3 \theta=2 \theta+\theta .\right)\) Derive a similar formula for \(\sin 3 \theta\) in terms of \(\sin \theta\).
https://wits.mathsgee.com/524/prove-theta-theta-right-derive-similar-formula-theta-terms
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/524/prove-theta-theta-right-derive-similar-formula-theta-termsThu, 02 Sep 2021 01:16:34 +0000Derive the following identities by putting \(C=A+B\) and \(D=A-B\) (and expressing \(A\) and \(B\) in terms of \(C\) and \(D)\)
https://wits.mathsgee.com/523/derive-following-identities-putting-expressing-and-terms
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/523/derive-following-identities-putting-expressing-and-termsThu, 02 Sep 2021 01:15:32 +0000Use double angle formulae to prove the identities
https://wits.mathsgee.com/522/use-double-angle-formulae-to-prove-the-identities
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/522/use-double-angle-formulae-to-prove-the-identitiesThu, 02 Sep 2021 01:14:38 +0000If \(m=\sec \theta+p \tan \theta\) and \(n=p \sec \theta+\tan \theta\), prove that \(m^{2}-n^{2}=1-p^{2}\)
https://wits.mathsgee.com/521/if-m-sec-theta-p-tan-theta-and-n-p-sec-theta-tan-theta-prove-that
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/521/if-m-sec-theta-p-tan-theta-and-n-p-sec-theta-tan-theta-prove-thatThu, 02 Sep 2021 01:13:38 +0000Find \(\tan \theta\) if \(9 \sin ^{2} \theta-\cos ^{2} \theta=7\). (Divide through by \(\left.\cos ^{2} \theta .\right)\)
https://wits.mathsgee.com/520/find-theta-sin-theta-cos-theta-divide-through-left-theta-right
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/520/find-theta-sin-theta-cos-theta-divide-through-left-theta-rightThu, 02 Sep 2021 01:13:01 +0000Derive the formula \(\cos A \cos B=\frac{1}{2}(\cos (A+B)+\cos (A-B))\)
https://wits.mathsgee.com/519/derive-the-formula-cos-a-cos-b-frac-1-2-cos-a-b-cos-a-b
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/519/derive-the-formula-cos-a-cos-b-frac-1-2-cos-a-b-cos-a-bThu, 02 Sep 2021 01:12:01 +0000Find an expression for \(\sin ^{4} \theta\) in terms of cos of multiples of \(\theta\)
https://wits.mathsgee.com/518/find-an-expression-for-sin-theta-in-terms-cos-multiples-theta
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/518/find-an-expression-for-sin-theta-in-terms-cos-multiples-thetaThu, 02 Sep 2021 01:11:13 +0000Express \(\cos ^{2} \theta\) in terms of \(\cos 2 \theta\)
https://wits.mathsgee.com/517/express-cos-2-theta-in-terms-of-cos-2-theta
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/517/express-cos-2-theta-in-terms-of-cos-2-thetaThu, 02 Sep 2021 01:10:38 +0000Express \(\sin ^{2} \theta\) in terms of \(\cos 2 \theta\)
https://wits.mathsgee.com/516/express-sin-2-theta-in-terms-of-cos-2-theta
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/516/express-sin-2-theta-in-terms-of-cos-2-thetaThu, 02 Sep 2021 01:10:03 +0000What is the double angle formulae in trigonometry?
https://wits.mathsgee.com/514/what-is-the-double-angle-formulae-in-trigonometry
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/514/what-is-the-double-angle-formulae-in-trigonometryThu, 02 Sep 2021 01:08:32 +0000What are compound angle identities?
https://wits.mathsgee.com/512/what-are-compound-angle-identities
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/512/what-are-compound-angle-identitiesThu, 02 Sep 2021 01:07:08 +0000What are some of the trigonometric identities derived from the unit circle?
https://wits.mathsgee.com/510/what-some-trigonometric-identities-derived-from-unit-circle
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/510/what-some-trigonometric-identities-derived-from-unit-circleThu, 02 Sep 2021 01:05:44 +0000Use the sketch of the unit circle to check the following trigonometric properties:
https://wits.mathsgee.com/509/sketch-unit-circle-check-following-trigonometric-properties
<p>Use the sketch of the unit circle to check the following trigonometric properties:</p>
<p><strong>half revolution</strong></p>
<p>\[
<br>
\left.\begin{array}{l}
<br>
\cos (\theta+\pi)=-\cos \theta \\
<br>
\sin (\theta+\pi)=-\sin \theta
<br>
\end{array}\right\}
<br>
\]</p>
<p><strong>same point</strong></p>
<p>\[
<br>
\left.\begin{array}{l}
<br>
\cos (\theta+2 \pi)=\cos \theta \\
<br>
\sin (\theta+2 \pi)=\sin \theta
<br>
\end{array}\right\}
<br>
\]</p>
<p> </p>MATH1042A (Engineering)https://wits.mathsgee.com/509/sketch-unit-circle-check-following-trigonometric-propertiesThu, 02 Sep 2021 01:04:09 +0000What are some of the special angles in radians?
https://wits.mathsgee.com/507/what-are-some-of-the-special-angles-in-radians
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/507/what-are-some-of-the-special-angles-in-radiansThu, 02 Sep 2021 01:00:34 +0000Find partial fractions for the following rational functions, evaluating all constants:
https://wits.mathsgee.com/506/fractions-following-rational-functions-evaluating-constants
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/506/fractions-following-rational-functions-evaluating-constantsThu, 02 Sep 2021 00:59:22 +0000Write down the partial fractions of \(\dfrac{x^{4}+1}{\left(x^{2}-2 x+3\right)^{2}}\)
https://wits.mathsgee.com/505/write-down-the-partial-fractions-of-dfrac-1-left-x-2-2-x-3-right
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/505/write-down-the-partial-fractions-of-dfrac-1-left-x-2-2-x-3-rightThu, 02 Sep 2021 00:58:20 +0000Write down the partial fractions of \(\dfrac{x^{3}+3 x+1}{x^{2}-x-2}\)
https://wits.mathsgee.com/504/write-down-the-partial-fractions-of-dfrac-x-3-3-x-1-x-2-x-2
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/504/write-down-the-partial-fractions-of-dfrac-x-3-3-x-1-x-2-x-2Thu, 02 Sep 2021 00:57:01 +0000Express in partial fractions: \[ \frac{x}{(x-1)\left(x^{2}+1\right)^{2}} \]
https://wits.mathsgee.com/503/express-in-partial-fractions-frac-x-x-1-left-x-2-1-right-2
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/503/express-in-partial-fractions-frac-x-x-1-left-x-2-1-right-2Thu, 02 Sep 2021 00:55:36 +0000Is \(\frac{x^{3}}{(x+1)(x-3)}\) a proper fraction?
https://wits.mathsgee.com/501/is-frac-x-3-x-1-x-3-a-proper-fraction
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/501/is-frac-x-3-x-1-x-3-a-proper-fractionThu, 02 Sep 2021 00:53:54 +0000What is the difference between a proper and improper fraction?
https://wits.mathsgee.com/499/what-is-the-difference-between-proper-and-improper-fraction
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/499/what-is-the-difference-between-proper-and-improper-fractionThu, 02 Sep 2021 00:51:10 +0000What are repeated linear Factors?
https://wits.mathsgee.com/498/what-are-repeated-linear-factors
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/498/what-are-repeated-linear-factorsThu, 02 Sep 2021 00:49:48 +0000Split \[ \frac{x+3}{(x-2)(x+4)} \] into 2 partial fractions, one with denominator \((x-2)\) and the other with denominator \((x+4)\).
https://wits.mathsgee.com/497/split-frac-partial-fractions-denominator-other-denominator
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/497/split-frac-partial-fractions-denominator-other-denominatorThu, 02 Sep 2021 00:48:43 +0000How do I express \(\dfrac{2}{x+1}+\dfrac{x}{x^{2}+1}\) as a single fraction?
https://wits.mathsgee.com/495/how-do-i-express-dfrac-2-x-1-dfrac-x-x-2-1-as-a-single-fraction
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/495/how-do-i-express-dfrac-2-x-1-dfrac-x-x-2-1-as-a-single-fractionThu, 02 Sep 2021 00:45:14 +0000Use the Remainder Theorem to find linear factors for the polynomials below. Once you are down to a quadratic, you can use the quadratic formula instead.
https://wits.mathsgee.com/494/remainder-factors-polynomials-quadratic-quadratic-instead
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/494/remainder-factors-polynomials-quadratic-quadratic-insteadThu, 02 Sep 2021 00:43:34 +0000What is the fundamental theorem of algebra?
https://wits.mathsgee.com/492/what-is-the-fundamental-theorem-of-algebra
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/492/what-is-the-fundamental-theorem-of-algebraThu, 02 Sep 2021 00:41:55 +0000Use the remainder theorem to factorise the following:
https://wits.mathsgee.com/491/use-the-remainder-theorem-to-factorise-the-following
<p>Use the remainder theorem to factorise the following:</p>
<ol>
<li>\(a(x)=x^{3}-7 x+6\)</li>
<li>\(a(x)=x^{6}-6 x^{4}+9 x^{2}-4\)</li>
</ol>MATH1042A (Engineering)https://wits.mathsgee.com/491/use-the-remainder-theorem-to-factorise-the-followingThu, 02 Sep 2021 00:41:17 +0000Prove the remainder theorem of polynomials
https://wits.mathsgee.com/489/prove-the-remainder-theorem-of-polynomials
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/489/prove-the-remainder-theorem-of-polynomialsThu, 02 Sep 2021 00:37:01 +0000State the remainder theorem of polynomials
https://wits.mathsgee.com/487/state-the-remainder-theorem-of-polynomials
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/487/state-the-remainder-theorem-of-polynomialsThu, 02 Sep 2021 00:35:24 +0000Simplify \(5 x^{2}-30 x-2\) by completing the square.
https://wits.mathsgee.com/486/simplify-5-x-2-30-x-2-by-completing-the-square
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/486/simplify-5-x-2-30-x-2-by-completing-the-squareThu, 02 Sep 2021 00:34:37 +0000Simplify \(x^{2}-10 x+4\) by completing the square.
https://wits.mathsgee.com/485/simplify-x-2-10-x-4-by-completing-the-square
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/485/simplify-x-2-10-x-4-by-completing-the-squareThu, 02 Sep 2021 00:34:12 +0000Simplify \(x^{2}+6 x+5\) by completing the square.
https://wits.mathsgee.com/484/simplify-x-2-6-x-5-by-completing-the-square
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/484/simplify-x-2-6-x-5-by-completing-the-squareThu, 02 Sep 2021 00:33:38 +0000Describe the process of simplifying a quadratic expression using the approach of "completing the square".
https://wits.mathsgee.com/482/describe-simplifying-quadratic-expression-approach-completing
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/482/describe-simplifying-quadratic-expression-approach-completingThu, 02 Sep 2021 00:31:09 +0000Solve \(\dfrac{1}{x-8}-\dfrac{1}{x-3}=\dfrac{1}{x-7}-\dfrac{1}{x-2}\)
https://wits.mathsgee.com/481/solve-dfrac-1-x-8-dfrac-1-x-3-dfrac-1-x-7-dfrac-1-x-2
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/481/solve-dfrac-1-x-8-dfrac-1-x-3-dfrac-1-x-7-dfrac-1-x-2Thu, 02 Sep 2021 00:29:36 +0000Solve \(\dfrac{x}{x-1}+1=\dfrac{x-2}{2 x}\)
https://wits.mathsgee.com/480/solve-dfrac-x-x-1-1-dfrac-x-2-2-x
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/480/solve-dfrac-x-x-1-1-dfrac-x-2-2-xThu, 02 Sep 2021 00:28:42 +0000Solve \(\dfrac{x+1}{x^{2}-5 x+6}=\dfrac{x-1}{x^{2}+x-12}\)
https://wits.mathsgee.com/479/solve-dfrac-x-1-x-2-5-x-6-dfrac-x-1-x-2-x-12
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/479/solve-dfrac-x-1-x-2-5-x-6-dfrac-x-1-x-2-x-12Thu, 02 Sep 2021 00:27:53 +0000Simplify \(\dfrac{7}{x^{2}-5 x+6}-\dfrac{6}{x^{2}+2 x-8}\)
https://wits.mathsgee.com/478/simplify-dfrac-7-x-2-5-x-6-dfrac-6-x-2-2-x-8
[no viewer found for format: markdown]MATH1042A (Engineering)https://wits.mathsgee.com/478/simplify-dfrac-7-x-2-5-x-6-dfrac-6-x-2-2-x-8Thu, 02 Sep 2021 00:27:03 +0000