8.1 & 8.2 - Radians, Arc Length, and Unit Circle

Expressed in degrees, $\frac{26\pi}{9}$  radians is equivalent to: 

• 9°

• 0.158°

• 520°

• 165.5°

Answer explanation

To convert from radians to degrees, multiply the radian by  $\frac{180}{\pi}$ .  

Type:  $\frac{26\pi}{9}\cdot\frac{180}{\pi}$  in Desmos to get this result.

Tags

CCSS.HSF.TF.A.1

Expressed in radians, 310° is approximately equivalent to:

• 5.41 radians

• 1.72 radians

• 0.86 radians

• 2.71 radians

Answer explanation

Tags

CCSS.HSF.TF.A.1

A circle has a diameter of 14 inches. What is the radian measure of a central angle that intercepts an arc of length 21 inches?

• 3 radians

• 1.5 radians

• 171.9 radians

• 147 radians

Answer explanation

Tags

CCSS.HSG.SRT.C.8

A circle has a radius of 9 inches. What is the length of an arc subtended by a central angle of $\frac{5\pi}{8}$  radians? Round to the nearest hundredth of an inch.

• 8.83 inches

• 35.34 inches

• 26.28 inches

• 17.67 inches

Answer explanation

Tags

CCSS.HSG.C.B.5

What is $\sin\left(\frac{\pi}{3}\right)$  ?

•  $\frac{1}{2}$  

•  $-\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$  

•  $-\frac{\sqrt{3}}{2}$  

•  $\frac{\sqrt{2}}{2}$  

Answer explanation

 $\frac{\pi}{3}$  is a radian. 

Tags

CCSS.HSF.TF.A.2

If sin(θ) = cos(θ), in which quadrants of the unit circle could the terminal side of θ be located?

Select all the apply.

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Answer explanation

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CCSS.HSF.TF.A.2

On a unit circle, the ordered pair (x, y) represents the point where the terminal side of θ intersects the unit circle. If m∠θ = 3π/4, what is the value of x in simplest form?

• $\frac{\sqrt{2}}{2}$

• $-\frac{\sqrt{3}}{2}$

• $1$

• $-\frac{1}{2}$

• $-\frac{\sqrt{2}}{2}$

Answer explanation

Tags

CCSS.HSF.TF.A.2

On a unit circle, the ordered pair (x, y) represents the point where the terminal side of θ intersects the unit circle. If m∠θ = 120°, what is the value of y in simplest form?

• $\frac{\sqrt{2}}{2}$

• $\frac{\sqrt{3}}{2}$

• $-\frac{\sqrt{3}}{2}$

• $0$

• $-1$

Answer explanation

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CCSS.HSF.TF.A.2

In the unit circle pictured, what is the sine of t?

•  $\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$  

•  $\frac{\sqrt{2}}{2}$  

•  $\frac{1}{\sqrt{3}}$  

•  $2$  

Answer explanation

Sine (sin for short) is the y-value, which is 1/2 in this picture. No work or calculations necessary. 

Tags

CCSS.HSF.TF.A.2

The diagram below shows an angle, θ, graphed in the xy-coordinate plane. Segment RT is the initial side of the angle, and segment RM is the terminal side. Segments RT and RM are radii of the unit circle centered at the origin R(0, 0).The x-coordinate of point M is  $-\frac{1}{2}$ 

What is the measure of θ to the nearest thousandth of a radian?

• 4.712

• 4.189

• 3.927

• 3.665

Answer explanation

Let's go over this one in class together!

Tags

CCSS.HSF.TF.A.1