Review Unit Circle

​Evaluating Unit Circle

By Haeyeon Kim

Multiple Choice

$$\csc\left(\frac{7\pi}{6}\right)=$$  

• $$\frac{1}{2}$$  

• $$-\frac{1}{2}$$  

• 2

• -2

Multiple Choice

$$\cos\left(\frac{35\pi}{6}\right)=$$  

• $$\frac{\sqrt[]{3}}{2}$$  

• $$-\frac{\sqrt[]{3}}{2}$$  

• -1/2

• 1

• 0

Multiple Select

Find the value of $$\theta$$ when $$\sin\theta=1$$

• $$\frac{\pi}{2}$$

• $$\frac{3\pi}{2}$$

• $$\frac{9\pi}{2}$$

• $$-\frac{\pi}{2}$$

Multiple Select

Find the value of $$\theta$$ when $$\sec\theta=undefined$$

• $$\frac{\pi}{2}$$

• $$\frac{3\pi}{2}$$

• $$\pi$$

• $$-\frac{5\pi}{3}$$

Multiple Select

Find the value of $$\theta$$ when $$\tan\theta=\frac{\sqrt[]{3}}{3}$$

• $$\frac{\pi}{6}$$

• $$\frac{5\pi}{3}$$

• $$\frac{7\pi}{6}$$

• $$-\frac{2\pi}{3}$$

• $$\frac{5\pi}{6}$$

Multiple Select

Find the value of $$\theta$$ when $$\cos\theta=-\frac{1}{2}$$

• $$\frac{2\pi}{3}$$

• $$\frac{5\pi}{3}$$

• $$\frac{4\pi}{3}$$

• $$-\frac{2\pi}{3}$$

• $$\frac{11\pi}{3}$$

Multiple Choice

$$\sin\left(-\frac{\pi}{4}\right)=$$  

• $$\sqrt{2}$$  

• $$-\sqrt{2}$$  

• $$\frac{\sqrt{2}}{2}$$  

• $$-\frac{\sqrt{2}}{2}$$  

Multiple Choice

$$\tan\left(-\frac{19\pi}{3}\right)=$$  

• $$-1$$  

• $$-\sqrt[]{3}$$  

• $$-\frac{\sqrt{3}}{3}$$  

• $$\frac{\sqrt{3}}{3}$$  

• $$\sqrt[]{3}$$

Multiple Choice

cosθ is positive in

• the 1st and 2nd quadrants
• the 1st and 3rd quadrants
• the 1st and 4th quadrants
• the 2nd and 3rd quadrants

Multiple Choice

What is the exact coordinates of  3π/4 on the unit circle?

• (−√2∕2, √2∕2)
• (−√2∕2, −√2∕2)
• (−√3∕2, −√2∕2)
• (√2∕2, −√2∕2)

Multiple Choice

What is the exact coordinates of  5π/3 on the unit circle?

• (−√3∕2, √2∕2)

• (1∕2, −√3∕2)

• (−√3∕2, −1∕2)

• (-1∕2, −√3∕2)

Multiple Choice

What is the exact coordinates of  7π/6 on the unit circle?

• (−√2∕2, √2∕2)
• (−1∕2, −3∕2)

• (−√3∕2, −1∕2)

• (-√2∕2, −√2∕2)

Multiple Choice

tan 7π/4

• -1
• 1
• √2/2
• undefined

Multiple Choice

sin 15π

• -1
• 1
• 1/2

• undefined
• 0

Multiple Choice

$$\cot\ 3\pi$$

• -1
• 1
• 1/2

• undefined
• 0