Quiz about Identities, Trigonometric equations and Vectors REvision

Question 1

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

Accepted Answer

$$\sin\ 60^{o\ }$$

Answer

$$\sin\ 90^{o\ }$$

Answer

$$\cos\ 90^{o\ }$$

Answer

$$\cos\ 60^{o\ }$$

Question 2

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

Accepted Answer

$$\cos100^{o\ }$$

Answer

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

Answer

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

Answer

$$\cos^2100^{o\ }$$

Question 3

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 4

$$\frac{ an45^o+ an30^o}{1- an45^o an30^o}$$ is equivalent to

Accepted Answer

$$ an75^o$$

Answer

$$ an\ 15^o$$

Answer

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

Answer

$$ an90^{o\ }$$

Question 5

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 6

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 7

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 8

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 9

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

Accepted Answer

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

Answer

$$\sqrt{2}$$

Answer

$$\sqrt{3}$$

Answer

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

Question 10

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

Accepted Answer

$$4\sin60^o$$

Answer

$$4\sin15^o$$

Answer

$$4\cos60^o$$

Answer

$$4\cos15^o$$

Question 11

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

Accepted Answer

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

Answer

$$\frac{3}{2}$$

Answer

$$\frac{9}{16}$$

Answer

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

Question 12

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

Accepted Answer

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

Answer

$$\pi$$

Answer

DNE

Answer

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

Question 13

write in component form

Accepted Answer

<11, 13>

Answer

<9, 15>

Answer

<7, 17>

Answer

<15, 9>

Question 14

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

Accepted Answer

$$\sqrt[]{530}$$

Answer

$$\sqrt[]{445}$$

Answer

$$\sqrt[]{234}$$

Answer

23

Question 15

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

Accepted Answer

12.81

Answer

2

Answer

6

Answer

18

Question 16

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

Accepted Answer

<5, -10>

Answer

<-10, 5>

Answer

<4, -5>

Answer

<-6, 10>

Question 17

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

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