Free Printable Unit 6 Day 2 Practice

1.

$2\sin\left(10\right)\cos\left(10\right)=$

a)

$\sin\left(5\right)\cos\left(5\right)$

b)

$\sin\left(20\right)\cos\left(20\right)$

c)

$\cos\left(20\right)$

d)

$\sin\left(20\right)$

2.

$\csc\theta=-\frac{\sqrt{13}}{2}$ and $\pi<\theta<\frac{3\pi}{2}$ . Find $\tan2\theta$

a)

$\frac{401\sqrt{465}}{7440}$

b)

$\frac{5}{12}$

c)

$\frac{7}{24}$

d)

$\frac{12}{5}$

3.

Solve the following equation using any Identities for $0\le\theta<2\pi$ :
$\cos2\theta=\cos\theta$

a)

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

b)

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

c)

$\frac{\pi}{2},\frac{5\pi}{6},\frac{7\pi}{6}$

d)

$0,\frac{5\pi}{6},\frac{7\pi}{6}$

4.

Solve the equation for all solutions:

\cos\frac{x}{3}=\frac{1}{2}

a)

$\pi+6\pi k\ and\ 5\pi+6\pi k$

b)

$\frac{\pi}{3}+2\pi k\ and\ \frac{5\pi}{3}+2\pi k$

c)

$\frac{\pi}{3}+2\pi\pi$

d)

$\pi+6\pi k$

5.

$\cos^2\left(10\right)-\sin^2\left(10\right)=$

a)

$\cos\left(20\right)$

b)

$\sin\left(20\right)$

c)

1

d)

$\cos\left(100\right)-\sin\left(100\right)$

6.

$\cos\theta=\frac{4}{5}\ \ and\ \ \frac{3\pi}{2}<\theta<2\pi$

Find the exact value of $\sin2\theta$ .

a)

$-\frac{1}{5}$

b)

$\frac{24}{25}$

c)

$-\frac{24}{25}$

d)

$-\frac{25}{24}$

7.

Solve the equation for all solutions:

\tan3x=1

a)

$\frac{\pi}{4}+2\pi k$

b)

$\frac{\pi}{12}+\frac{2\pi}{3}k$

c)

$\frac{\pi}{4}+\pi k$

d)

$\frac{\pi}{12}+\frac{\pi}{3}k$

8.

$\frac{2\tan\left(40\right)}{1-\tan^2\left(40\right)}=$

a)

$\frac{\tan\left(80\right)}{1-\tan\left(1600\right)}$

b)

$\tan\left(40\right)$

c)

$\tan\left(80\right)$

d)

$2\tan\left(40\right)$

9.

Solve the following equation using any Identities for $0\le x<2\pi$ :

\cos2x+3\sin x-2=0

a)

$0,\ \frac{\pi}{6},\frac{5\pi}{6}$

b)

$\frac{\pi}{2},\frac{\pi}{6},\frac{5\pi}{6}$

c)

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

d)

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

10.

$\sin x=\frac{12}{13}\ \ and\ \ \frac{\pi}{2}<x<\pi$

Find the exact value of $\cos2x$ .

a)

$-\frac{120}{169}$

b)

$\frac{119}{169}$

c)

$-\frac{119}{169}$

d)

$\frac{120}{119}$

11.

Write as a single trig function of a single angle.
$2\sin\frac{\pi}{5}\cos\frac{\pi}{5}$

a)

$\sin\frac{\pi}{10}$

b)

$\sin\frac{2\pi}{5}$

c)

$\cos\frac{2\pi}{5}$

d)

$\cos\frac{\pi}{10}$

12.

Solve the following equation using any Identities for $0\le x<2\pi$ : $\sin x=\cos2x$

a)

$\frac{\pi}{6},\frac{5\pi}{6},\frac{3\pi}{2}$

b)

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

c)

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

d)

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

13.

$\cos^2\ 15^o-\sin^2\ 15^o=$

Write as a single trigonometric expression.

a)

$\cos\left(15^{o^{ }}\right)$

b)

$\cos\left(30^o\right)$

c)

1

d)

$\tan^2\left(15^o\right)$

14.

a)

$\frac{4\sqrt{2}}{9}$

b)

$\frac{2}{3}$

c)

$\frac{4\sqrt{2}}{3}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{3}$

Unit 6 Day 2 Practice

Total questions: 14

Worksheet time: 2hrs 20mins

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