Free Printable Identities, Trigonometric equations and Vectors REvision

1.

Write as a single expression $\sin75^o\cos15^o-\cos75^{o\ }\sin15^o$

a)

$\sin\ 90^{o\ }$

b)

$\sin\ 60^{o\ }$

c)

$\cos\ 90^{o\ }$

d)

$\cos\ 60^{o\ }$

2.

Write as a single expression $1-2\sin^250^o$

a)

$2\sin\ 100^{o\ }$

b)

$\sin^2\ 50^{o\ }$

c)

$\cos^2100^{o\ }$

d)

$\cos100^{o\ }$

3.

Write as a single expression
$\cos\left(\frac{\pi}{3}\right)\cos\left(\frac{2\pi}{5}\right)-\sin\left(\frac{\pi}{3}\right)\sin\left(\frac{2\pi}{5}\right)$

a)

$\sin\left(\frac{11\pi}{5}\right)$

b)

$\cos\left(\frac{11\pi}{5}\right)$

c)

$\sin\left(\frac{\pi}{15}\right)$

d)

$\cos\left(\frac{\pi}{15}\right)$

4.

$\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}$ is equivalent to

a)

$\tan75^o$

b)

$\tan\ 15^o$

c)

$\frac{\sin45^o}{\cos30^o}$

d)

$\tan90^{o\ }$

5.

Use sum or difference angles identity to find the exact value for $\cos105^o$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{-\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

6.

Use sum or difference angle's identity to find the exact value for $\sin\ \left(15^o\right)$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

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

7.

Given $\sin x=\frac{3}{5}$ where x is an acute angle. $Evaluate\ \cos\left(\frac{\pi}{6}+x\right)$

a)

$\frac{4\sqrt{3}+3}{10}$

b)

$\frac{4\sqrt{3}-3}{10}$

c)

$\frac{2\sqrt{5}+12}{15}$

d)

$\frac{4\sqrt{5}+2}{5}$

8.

Write as a single expression $\sqrt{\frac{1-\cos15\degree}{2}}$

a)

$\sin\left(\frac{30\degree}{2}\right)$

b)

$\cos\left(\frac{30\degree}{2}\right)$

c)

$\sin\left(\frac{15\degree}{2}\right)$

d)

$\cos\left(\frac{15\degree}{2}\right)$

9.

If $\cos A=\frac{1}{3}$ , then the positive value of $\tan\ \frac{A}{2}$ ?

a)

$\sqrt{2}$

b)

$\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

$\frac{\sqrt{2}}{2}$

10.

The expression $8\sin30^o\cos30^o$ has the same value as

a)

$4\sin15^o$

b)

$4\cos60^o$

c)

$4\sin60^o$

d)

$4\cos15^o$

11.

If $\cos\theta=\frac{1}{8},$ the positive value of $\sin\ \frac{\theta}{2}$ is

a)

$\frac{3}{2}$

b)

$\frac{\sqrt{7}}{4}$

c)

$\frac{9}{16}$

d)

$\frac{3}{4}$

12.

Solve $2\cos^2\theta+\cos\theta=0$ the equation over for $0<\theta<2\pi$

choose all correct answers.

a)

π/2, 3π/2

b)

0, π,2π

c)

2π/3, 4π/3

d)

π/3, 5π/3

13.

Solve $\sin\theta\tan\theta=\sin\theta$ the equation over for $0<\theta<2\pi$

choose all correct answers.

a)

π/2, 3π/2

b)

3π/4, 7π/4

c)

0, π

d)

π/4, 5π/4

14.

Solve $2\sin^2\theta-5\sin\theta+2=0$ the equation over for $0<\theta<2\pi$

a)

π/6, 5π/6

b)

7π/6, 11π/6

c)

π/3, 2π/3

d)

4π/3, 5π/3

15.

Solve $5\cos\theta+\sqrt{2}=3\cos\theta$ the equation over for $0<\theta<\pi$

a)

$\pi$

b)

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

c)

DNE

d)

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

16.

Solve $\sin\theta+\cos\theta=0$ the equation over for $0<\theta<\pi$

a)

2π/3

b)

3π/4

c)

5π/6

d)

2π

17.

write in component form

a)

<9, 15>

b)

<7, 17>

c)

<15, 9>

d)

<11, 13>

18.

Given u = <3, 7> and v =<-5, 4>, find |2v - 3u|

a)

$\sqrt[]{445}$

b)

$\sqrt[]{530}$

c)

$\sqrt[]{234}$

d)

23

19.

Find the magnitude of the vector <10, -8>

a)

2

b)

12.81

c)

6

d)

18

20.

If w = <2, -5> and y = <2, 0>, find 2w + 0.5y

a)

<-10, 5>

b)

<4, -5>

c)

<-6, 10>

d)

<5, -10>

21.

Determine the direction and magnitude of the vector 〈-11,5〉

Round your answers to the nearest tenth.

a)

Direction 24.4°
Vertical 12.1

b)

Direction65.6°
Magnitude 12.1

c)

Direction -24.4°
Magnitude 12.1

d)

Direction 155.6°
Magnitude 12.1

22.

Find a unit vector in the direction of <6, -8>

a)

$<\frac{3}{5},-\frac{4}{5}>$

b)

$<\frac{3}{50},-\frac{4}{50}>$

c)

$<\frac{1}{10},-\frac{1}{10}>$

d)

$<\frac{1}{6},\ -\frac{1}{8}>$

Identities, Trigonometric equations and Vectors REvision

Total questions: 22

Worksheet time: 52mins

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