Circles and conic sections

Which degree is equivalent to  $\frac{\pi}{4}$  ?

•  $210\degree$  

•  $45\degree$  

•  $150\degree$  

•  $60\degree$  

• 54 degrees

• 169.6 degrees

• 2.96 degrees

• 62 degrees

**What is 2π/3 radians in degrees?

• 150

• 120

• 180

• 30

What is 2π/3 radians in degrees? 

(a)  

Identify the radian and degree measure at D.

• π/3

• 60^o

• π/6

• 30^o

• π/7

What is 3π/4 radians in degrees?

Mathematical Equivalence

ON

convert  $\frac{10\pi}{9}$  rad into degrees

•  $200\degree$  

•  $190\degree$  

•  $230\degree$  

•  $245\degree$  

Convert 3π/4 to degrees

• 147.3°
• 135°
• 125°
• 173.8°

What is the equivalent radian measure of 230 degrees?

• $\frac{5\pi}{18}$

• $-\frac{5\pi}{18}$

• $\frac{23\pi}{18}$

• $-\frac{23\pi}{18}$

What is the radian-measure angle equivalent to $210\degree$ 

?

•  $\frac{7\pi}{6}$  radians, or about 3.67 radians.

•  $\frac{5\pi}{6}$  radians, or about 2.62 radians.

•  $\frac{4\pi}{3}$  radians, or about 4.19 radians.

•  $\frac{2\pi}{3}$  radians, or about 2.09 radians.

Answer explanation

Mental math style: $210\degree\ =180\degree+30\degree$  , and  $180\degree=\pi$  radians,  $30\degree=\frac{\pi}{6}$  radians, so  $210\degree=\left(\pi+\frac{\pi}{6}\right)=\frac{7\pi}{6}$  radians.  Using the proportion  $\frac{\pi}{180}=\frac{\theta R}{210\degree}$   ,  $\theta R=\frac{210\cdot\pi}{180}=\frac{7\pi}{6}$  radians.