Q1
Answer
Express the following in terms of (positive) acute angles:
  1. $\sin240^{\circ}$
  2. $\cos(-50^{\circ})$
  3. $\tan600^{\circ}$
  1. $-\sin120^{\circ}$
  2. $\cos50^{\circ}$
  3. $\tan60^{\circ}$
Q2
Answer
Write the following in terms of $\sin\theta$, $\cos\theta$, or $\tan\theta$ only:
  1. $\sin(180^{\circ}-\theta)$
  2. $\cos(\theta-540^{\circ})$
  3. $\tan(540^{\circ}-\theta)$
  1. $\sin\theta$
  2. $-\cos\theta$
  3. $-\tan\theta$
Q3
Answer
Find the exact values of:
  1. $\cos495^{\circ}$
  2. $\tan(-225^{\circ})$
  3. $\sin(-60^{\circ})$
  1. $-\dfrac{\sqrt{2}}{2}$
  2. $-1$
  3. $-\dfrac{\sqrt{3}}{2}$
Q4
Answer
Simplify:
  1. $1-\cos^2\frac{1}{2}\theta$
  2. $5\sin^23\theta+5\cos^23\theta$
  1. $\sin^2\frac{1}{2}\theta$
  2. $5$
Q5
Answer
Simplify:
  1. $(1+\sin x)^2+(1-\sin x)^2+2\cos^2x$
  2. $\sin^4\theta+\sin^2\theta\cos^2\theta$
  1. $4$
  2. $\sin^2\theta$
Q6
Answer
Prove the following identities:
  1. $(\sin\theta+\cos\theta)^2\equiv2\sin\theta\cos\theta + 1$
  2. $\dfrac{1}{\cos\theta}-\cos\theta\equiv\sin\theta\tan\theta$
See video
Q7
Answer
Prove the following identities:
  1. $(2\sin\theta-\cos\theta)^2+(\sin\theta+2\cos\theta)^2\equiv5$
  2. $\sin^2x\cos^2y-\cos^2x\sin^2y\equiv\sin^2x-\sin^2y$
See video
Q8
Answer
Given $\tan\theta=\dfrac{5}{12}$ and $\theta$ is acute, find the exact value of:
  1. $\sin\theta$
  2. $\cos\theta$
  1. $\dfrac{5}{13}$
  2. $\dfrac{12}{13}$
Q9
Answer
Given $\cos\theta=-\dfrac{3}{5}$ and $\theta$ is obtuse, find the exact value of:
  1. $\sin\theta$
  2. $\tan\theta$
  1. $\dfrac{4}{5}$
  2. $-\dfrac{4}{3}$
Q10
Answer
Given $\sin\theta=-\dfrac{7}{25}$ and $270^{\circ}<\theta<360^{\circ}$, find the exact value of:
  1. $\cos\theta$
  2. $\tan\theta$
  1. $\dfrac{24}{25}$
  2. $-\dfrac{7}{24}$
Q11
Answer
For the following pair of equations, find a single equation in terms of $x$ and $y$, but not $\theta$: $$x=\sin\theta \quad y=\cos^2\theta$$
$x^2+y=1$
Q12
Answer
For the following pair of equations, find a single equation in terms of $x$ and $y$, but not $\theta$: $$x=\sin\theta+\cos\theta \quad y=\cos\theta-\sin\theta$$
$x^2+y^2=2$
Q13
Answer
Find the angle marked $x$ in the following triangle.
$79.9^{\circ}$
Q14
Answer
By first finding $x$, find the area of the following triangle.
$63.2$
Q15
Answer
By first finding $x$, find the area of the following triangle.
$258$
Q16
Answer
Find the reflex angle marked $x$ in the following triangle.
$302^{\circ}$
Q17
Answer
Calculate the area of a triangle with side lengths $10$, $13$, and $18$.
$63.5$
Q18
Answer
Find the area of the quadrilateral $ABCD$.
$25.6$