Use Unit Circle to find sine, cosine, tangent

Using the Unit Circle

• To use the Unit Circle to evaluate cosine, sine, or tangent we use the coordinates of the point of intersection between the terminal side of the angle and the Unit Circle.

• The x-coordinate of the point is equal to the cosine of the angle.

• The y-coordinate of the point is equal to the sine of the angle.

• To find the tangent of an angle you take the y-coordinate/x-coordinate.

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

Given the ordered pair (-¹/₂ , ^√3/₂), what is the value of cosine?

• √3

• ^-1/₂

• ^√3/₂

• ^√3/₃

Multiple Choice

What is cos 60°?

• ½

• ^√3/₂

• ^√2/₂

• 1

Multiple Choice

sin π/4

• √2∕2

• 1/2

• √3/2

• 0

Evaluate Tangent

• Tan(angle) = y-coordinate/x-coordinate

• Tangent is positive in the FIRST and THIRD quadrants.

• Tangent is negative in the SECOND and FOURTH quadrants.

• tan(90°) = 1/0 = UNDEFINED

• tan(π) = 0/-1 = 0

• tan(240°) = (-√3/2)/(-1/2)

• =(-√3/2) *(-2/1) = √3/1 = √3

Multiple Choice

What is tan 45°?

• 1

• ^√2/₂

• ^√3/₂

• ½

Multiple Choice

Evaluate $$\tan\left(\frac{\pi}{2}\right)$$  

• 0 

• 1 

•   $$\frac{1}{0}$$ undefined

•   $$\frac{0}{1}$$

Multiple Choice

Find the exact value of $$\tan\left(\frac{7\pi}{6}\right)$$   

• $$-\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{1}{\sqrt{\ 3}}$$

• $$-\frac{\sqrt{3}}{2}$$  

Multiple Choice

Using the reference angle, find the exact value of $$\tan\left(\frac{5\pi}{3}\right)$$  .

• $$-\frac{\sqrt[]{3}}{3}$$  

• $$-1$$  

• $$-\sqrt[]{3}$$  

• $$\sqrt[]{3}$$