Quiz about Daily Challenge 2: Sum and Difference Identities

Question 1

Evaluate: $$\sin\frac{5\pi}{12}$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 2

Evaluate: $$\sin\frac{7\pi}{12}$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 3

The circular points $$W\left(\frac{5\pi}{12}\right)$$ and $$W\left(\frac{7\pi}{12}\right)$$ have

Accepted Answer

the same y-coordinate but not the same x-coordinate

Answer

the same x- and y- coordinates

Answer

the same x-coordinate by not the same y-coordinate

Answer

do not have the same x- and y- coordinates

Question 4

Evaluate: $$\cos\frac{\pi}{12}$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

Evaluate: $$\cos\frac{11\pi}{12}$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 6

The values of $$\cos\frac{\pi}{12}$$ and $$\cos\frac{11\pi}{12}$$ only differ in sign because $$W\left(\frac{11\pi}{12}\right)$$ is the reflection of $$W\left(\frac{\pi}{12}\right)$$

Accepted Answer

with respect to the y-axis

Answer

with respect to the x-axis

Answer

with respect to the origin

Question 7

Which of the following is equal to $$ an\left(-75\degree ight)$$ ?

Accepted Answer

$$\frac{ an30\degree+ an45\degree}{ an30\degree an45\degree-1}$$

Answer

$$\frac{ an30\degree\ + an45\degree}{1- an30\degree an45\degree}$$

Answer

$$\frac{ an30\degree- an45\degree}{1+ an30\degree an45\degree}$$

Answer

$$\frac{ an45\degree- an30\degree}{1+ an45\degree an30\degree}$$

Question 8

Evaluate: $$ an\frac{2027\pi}{12}$$

Accepted Answer

$$\sqrt{3}-2$$

Answer

$$2+\sqrt{3}$$

Answer

$$2-\sqrt{3}$$

Answer

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

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