Unit Circle

The Unit Circle

What goes around, comes around

REMEMBER

• On the unit circle

   $\sin\ \theta\ =y$  and  $\cos\ \theta\ =\ x$  
  

•  $\cos^2\theta+\sin^2\theta=1$  and  $\tan\ \theta\ =\frac{\sin\theta}{\cos\ \theta}$  

Multiple Select

Which of the following is a point on the unit circle?

(Check all that apply)

•  $\left(1,\ 1\right)$  

•  $\left(-1,\ 0\right)$  

•  $\left(\frac{1}{\sqrt{2}},\ \frac{1}{\sqrt{2}}\right)$  

•  $\left(\frac{1}{\sqrt{5}},-\frac{2}{\sqrt{5}}\right)$  

Multiple Choice

Find the value of

 $\cos\ \theta$  if  $\sin\ \theta=-\frac{3}{\sqrt{10}},\ \pi<\theta<\frac{3\pi}{2}.$  

•  $\frac{1}{\sqrt{10}}$  

•  $\frac{4}{\sqrt{10}}$  

•  $-\frac{1}{\sqrt{10}}$  

•  $-\frac{4}{\sqrt{10}}$  

Points corresponding to $\frac{\pi}{2}$  and multiples

• (1, 0)

• (0, 1)

• (-1, 0)

• (0, -1)

Multiple Choice

Which of the following is an angle coterminal with $\frac{3\pi}{2}$  ?

•  $\frac{\pi}{3}$  

• - $\frac{\pi}{2}$  

•  $\frac{3\pi}{4}$  

•  $2\pi$  

Multiple Choice

 Which point on the unit circle corresponds to  $\frac{3\pi}{2}$  ?

• (0, 1)

• (1, 0)

• (0, -1)

• (-1, 0)

Multiple Choice

 $\sin\ \left(\frac{7\pi}{2}\right)\ =\ ?$  

Based on your unit circle,

• 1/2

• 0

• -1

• 1

Multiple Choice

 $\sec\ \frac{3\pi}{2}$  = ?

• 0

• undefined

• 1

• -1

Multiple Choice

 $\tan\ \pi$  = ?

• -1

• 0

• undefined

• √3

Multiple Choice

 $\sin\ 0\ =?$  

• 1

• -1

• 0

• √2/2

Common Points on the Unit Circle

•  $\frac{\pi}{4}\rightarrow\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)$  

•  $\frac{\pi}{3}\rightarrow\left(\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)$  

•  $\frac{\pi}{6}\rightarrow\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$  

Multiple Choice

What is the exact coordinates of   $\frac{3\pi}{4}$  on the unit circle?

• (−√2∕2, √2∕2)

• (−√2∕2, −√2∕2)

• (−√3∕2, −√2∕2)

• (√2∕2, −√2∕2)

Multiple Choice

 $\sin\ \frac{11\pi}{6}=?$  

• -1/2

• 1/2

• √3/2

• -√3/2

Multiple Choice

 $\cos\ \frac{4\pi}{3}=?$  

• -√3/2

• √3/2

• 1/2

• -1/2

Multiple Choice

What is the exact value of sin 150°

• -1/2
• -√3/2
• 1/2
• √3/2

Multiple Choice

What is the value of cosine at 315

• 0
• 1
• √2 / 2
• -√2 /2

Multiple Choice

 $\cos\ \frac{5\pi}{6}=?$  

• -1/2

• 1/2

• √3/2

• -√3/2

Multiple Choice

 $\sin\ \frac{2\pi}{3}=?$  

• 1/2

• -1/2

• √3/2

• -√3/2

Multiple Choice

csc 330⁰

• 2

• -2

• √2

• -√2

Multiple Choice

 $\tan\ \frac{\pi}{6}=?$  

• √3/3

• √3

• 1

• undefined

Multiple Choice

Find sin(-240°)

• (√3)/2)

• (-1/2)

• (√2/2)

• (1/2)