ACSEE (Form 6) Trigonometry — practice questions

Explore 3 free Trigonometry questions in ACSEE (Form 6) Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Trigonometry questions and exercises with answers

Showing questions 1–3 of 3.

Factorised using the factor formulae, $\cos\theta-\cos3\theta-\cos5\theta+\cos7\theta$ equals:Read the answer and worked solution →Given $\tan(2x+y)=2$ and $\tan 2x=\dfrac32$, the value of $\tan y$ is:Read the answer and worked solution →Signs in the second quadrantRead the answer and worked solution →

Worked practice questions

Factorised using the factor formulae, $\cos\theta-\cos3\theta-\cos5\theta+\cos7\theta$ equals:

$4\cos4\theta\sin2\theta\sin\theta$
$-4\sin4\theta\cos2\theta\cos\theta$
$-4\cos4\theta\sin2\theta\sin\theta$
$4\cos4\theta\cos2\theta\sin\theta$

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Correct answer: C. $-4\cos4\theta\sin2\theta\sin\theta$

1. Group the terms so each pair is a sum: $(\cos7\theta+\cos\theta)-(\cos5\theta+\cos3\theta)$. 2. Apply $\cos A+\cos B=2\cos\frac{A+B}{2}\cos\frac{A-B}{2}$ to both pairs. 3. This gives $2\cos4\theta\cos3\theta-2\cos4\theta\cos\theta$. 4. Factor out $2\cos4\theta$: $2\cos4\theta(\cos3\theta-\cos\theta)$. 5. Now $\cos3\theta-\cos\theta=-2\sin2\theta\sin\theta$, so the product is $-4\cos4\theta\sin2\theta\sin\theta$. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 5: Trigonometry_

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Given $\tan(2x+y)=2$ and $\tan 2x=\dfrac32$, the value of $\tan y$ is:

$\frac12$
$\frac18$
$\frac78$
$-\frac18$

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Correct answer: B. $\frac18$

1. Write $y$ as a difference: $y=(2x+y)-2x$. 2. Apply $\tan(A-B)=\dfrac{\tan A-\tan B}{1+\tan A\tan B}$ with $A=2x+y$ and $B=2x$. 3. Numerator: $2-\dfrac32=\dfrac12$. 4. Denominator: $1+2\times\dfrac32=1+3=4$. 5. So $\tan y=\dfrac{1/2}{4}=\dfrac18$. Subtracting the tangents directly, without the denominator, gives $\tfrac12$. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 5: Trigonometry_

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Signs in the second quadrant

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Questions

Question
Three of these statements about an obtuse angle x are false.
Choices
1. Item
  cos x is negative for obtuse x
  Correct
  Yes
2. Explanation
  sine stays positive in the second quadrant
  Item
  sin x is negative for obtuse x
3. Explanation
  tangent is negative in the second quadrant
  Item
  tan x is positive for obtuse x
4. Explanation
  an obtuse angle lies in quadrant 2
  Item
  an obtuse angle is in quadrant 1

Instructions

Three of these claims about an obtuse angle x are false. Fault them.

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