Quiz about Mastering Trigonometry: Sum, Difference, and Angle Formulas

Question 1

Use the sum formula to find $$\sin(75^\circ)$$ .

Accepted Answer

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

Answer

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

Answer

$$\frac{\sqrt{3} + 1}{2\sqrt{2}}$$

Answer

$$\frac{\sqrt{3} - 1}{2\sqrt{2}}$$

Question 2

What is $$\cos(2 heta)$$ if $$\cos( heta) = \frac{1}{2}$$ ?

Accepted Answer

$$-\frac{1}{2}$$

Answer

$$0$$

Answer

$$\frac{1}{4}$$

Answer

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

Question 3

Find the value of $$ an\left(\frac{\pi}{8} ight)$$ using the half-angle formula.

Accepted Answer

$$\sqrt{2} - 1$$

Answer

$$1 - \sqrt{2}$$

Answer

$$1 + \sqrt{2}$$

Answer

$$\sqrt{2} + 1$$

Question 4

Solve the equation $$\sin(2x) = \sqrt{2}/2$$ for $$0 \leq x \leq 2\pi$$ .

Accepted Answer

$$\frac{\pi}{8}, \frac{7\pi}{8}$$

Answer

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

Answer

$$\frac{\pi}{8}, \frac{3\pi}{8}$$

Answer

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

Question 5

Using the difference formula, find $$\cos(15^\circ)$$ .

Accepted Answer

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

Answer

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

Answer

$$\frac{\sqrt{3} + 1}{2\sqrt{2}}$$

Answer

$$\frac{\sqrt{3} - 1}{2\sqrt{2}}$$

Question 6

Graph the function $$y = 2\sin(2x)$$ for $$0 \leq x \leq 2\pi$$ .

Accepted Answer

A sine wave with amplitude 2, period $$\pi$$

Answer

A sine wave with amplitude 1, period $$2\pi$$

Answer

A sine wave with amplitude 2, period $$2\pi$$

Answer

A sine wave with amplitude 1, period $$\pi$$

Question 7

If $$ an( heta) = 1$$ , what is $$\sin(2 heta)$$ ?

Accepted Answer

$$1$$

Answer

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

Answer

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

Answer

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

Question 8

Using the sum formula, calculate $$\cos(105^\circ)$$ .

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 9

Solve for $$x$$ in the equation $$\cos^2(x) - \sin^2(x) = 0$$ for $$0 \leq x \leq 2\pi$$ .

Accepted Answer

$$\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}$$

Answer

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

Answer

$$0, \pi, 2\pi$$

Answer

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

Question 10

What is $$\sin\left(\frac{\pi}{12}\right)$$ using the difference formula?

Accepted Answer

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

Answer

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

Answer

$$\frac{\sqrt{3} - 1}{2\sqrt{2}}$$

Answer

$$\frac{\sqrt{3} + 1}{2\sqrt{2}}$$

Question 11

Calculate $$\cos\left(\frac{\pi}{6}\right)$$ using the sum formula.

Accepted Answer

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

Answer

$$\frac{1}{2}$$

Answer

$$1$$

Answer

$$0$$

Question 12

What is $$\sin(3 heta)$$ if $$\sin( heta) = \frac{1}{2}$$ ?

Accepted Answer

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

Answer

$$\frac{1}{2}$$

Answer

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

Answer

$$1$$

Question 13

Find the value of $$ an\left(\frac{3\pi}{4} ight)$$ using the half-angle formula.

Accepted Answer

$$-1$$

Answer

$$1$$

Answer

$$\sqrt{2}$$

Answer

$$-\sqrt{2}$$

Question 14

Calculate $$\sin\left(\frac{\pi}{3}\right)$$ using the sum formula.

Accepted Answer

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

Answer

$$\frac{1}{2}$$

Answer

$$1$$

Answer

$$0$$

Question 15

Find the value of $$\cos\left(\frac{5\pi}{6}\right)$$ using the half-angle formula.

Accepted Answer

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

Answer

$$-\frac{1}{2}$$

Answer

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

Answer

$$\frac{1}{2}$$

Question 16

What is $$\cos(3 heta)$$ if $$\cos( heta) = \frac{\sqrt{2}}{2}$$ ?

Accepted Answer

$$-\frac{1}{2}$$

Answer

$$0$$

Answer

$$\frac{1}{4}$$

Answer

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

Question 17

Calculate $$\cos\left(\frac{2\pi}{3}\right)$$ using the sum formula.

Accepted Answer

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

Answer

$$-\frac{1}{2}$$

Answer

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

Answer

$$\frac{1}{2}$$

Question 18

Find the value of $$\sin\left(\frac{7\pi}{6}\right)$$ using the half-angle formula.

Accepted Answer

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

Answer

$$-\frac{1}{2}$$

Answer

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

Answer

$$\frac{1}{2}$$

Question 19

Use the difference formula to find $$\sin(120^\circ)$$ .

Accepted Answer

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

Answer

$$\frac{1}{2}$$

Answer

$$1$$

Answer

$$0$$

Question 20

Calculate $$\cos\left(\frac{5\pi}{4}\right)$$ using the half-angle formula.

Accepted Answer

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

Answer

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

Answer

$$-\frac{1}{2}$$

Answer

$$\frac{1}{2}$$

Question 21

Find the value of $$\sin\left(\frac{\pi}{4}\right)$$ using the difference formula.

Accepted Answer

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

Answer

$$\frac{1}{2}$$

Answer

$$1$$

Answer

$$0$$

Question 22

What is $$ an(2 heta)$$ if $$ an( heta) = \frac{1}{\sqrt{3}}$$ ?

Accepted Answer

$$\frac{2\sqrt{3}}{3\sqrt{3}-1}$$

Answer

$$\frac{2\sqrt{3}}{3\sqrt{3}+1}$$

Answer

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

Answer

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

Mastering Trigonometry: Sum, Difference, and Angle Formulas

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