Free Printable Trigonometry - Identities and double angle formulas

1.

Solve $\cos2x-\cos x=0$ for $0\le x\le2\pi$ .

a)

$0,\ \frac{2\pi}{3},\ \frac{4\pi}{3},\ 2\pi$

b)

$\frac{5\pi}{6},\ \frac{7\pi}{6}$

c)

$\frac{\pi}{3},\ \frac{5\pi}{3}$

d)

$\frac{\pi}{4},\frac{3\pi}{4},\ \frac{5\pi}{4}$

2.

Given that $\sin\theta=-\frac{5}{6},\ \frac{3\pi}{2}\le\theta\le2\pi$ , find $\cos\ 2\theta$ .

a)

$\frac{10}{12}$

b)

$-\frac{5\sqrt{11}}{18}$

c)

$-\frac{7}{18}$

d)

$-\frac{10}{12}$

3.

If $\cos\beta=\frac{2}{5}$ where $270\degree\le\beta\le360\degree$ , find $\sin2\beta$ .

a)

$-\frac{4\sqrt{21}}{25}$

b)

$\frac{4\sqrt{21}}{25}$

c)

$\frac{4\sqrt{3}}{5}$

d)

$-\frac{4\sqrt{3}}{5}$

4.

Simplify $\frac{\sin\left(\pi-\theta\right)-\sin\left(-\theta\right)}{\cos\ \left(-\theta\right)}$

a)

$0$

b)

$2\tan\theta$

c)

$\frac{1}{\cos\ \theta}$

d)

$\tan\theta$

5.

Solve for $0\le x\le2\pi$ , $\sin x=\sin\ 2x$ .

a)

0

b)

$0,\ \frac{\pi}{3},\ \pi,\ \frac{5\pi}{3},\ 2\pi$

c)

$0,\ 2\pi$

d)

$0,\ \frac{\pi}{6},\frac{11\pi}{6},\ 2\pi$

6.

Solve $\sin\theta\cos\theta=\frac{1}{4}$ for $-\pi\le\theta\le\pi$ .

a)

$\pm\frac{\pi}{12},\pm\frac{5\pi}{12}$

b)

$-\frac{7\pi}{6},-\frac{11\pi}{6},\frac{\pi}{6},\ \frac{5\pi}{6}$

c)

$\pm\frac{\pi}{6},\pm\frac{5\pi}{6}$

d)

$-\frac{11\pi}{12},-\frac{7\pi}{12},\frac{\pi}{12},\frac{5\pi}{12}$

7.

If $\sin\theta=\frac{4}{5}$ and $\cos\theta=\frac{3}{5}$ find $\tan2\theta$ .

a)

$-\frac{7}{24}$

b)

$\frac{24}{7}$

c)

$\frac{7}{24}$

d)

$-\frac{24}{7}$

8.

Simplify $\left(2\sin\theta+3\cos\theta\right)^2+\left(3\sin\theta-2\cos\theta\right)^2$ .

a)

$5$

b)

18

c)

13

d)

$13\sin^2\ \theta\ +\ 24\sin\theta\cos\theta+13\cos^2\ \theta$

9.

If $\sin\alpha=-\frac{2}{3}$ , find $\cos2\alpha$ .

a)

$\frac{5}{9}$

b)

$\frac{7}{3}$

c)

$\frac{1}{9}$

d)

$\frac{8}{9}$

10.

Find the exact answer of $\left(\cos\ \frac{\pi}{12}+\sin\ \frac{\pi}{12}\right)^2$ .

a)

$-\frac{1}{2}$

b)

$1$

c)

$\frac{1}{2}$

d)

$\frac{3}{2}$

Trigonometry - Identities and double angle formulas

Total questions: 10

Worksheet time: 3hrs 30mins

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