Evaluating Trig Ratios with the Unit Circle

Evaluating Sine & Cosine with the Unit Circle

Goal: Students will be able to evaluate sine and cosine using the Unit Circle

Using the Unit Circle

• to evaluate sine and cosine, we use the coordinates that lie on the Unit Circle's circumference

• cosine of an angle is equal to the length of the reference triangle's adjacent side and is represented by the x-coordinate

• sine of an angle is equal to the length of the reference triangle's opposite side and is represented by the y-coordinate

Evaluating Cosine

• cos(θ) = x-coordinate of the point associated with that angle

• cos(270°) = 0

• cos(π/6) = √3/2

• cos(2π/3) = -1/2

Multiple Choice

Evaluate cos(135°)

•  $-\frac{\sqrt{2}}{2}$  

•  $\frac{\sqrt{2}}{2}$  

•  $-\frac{\sqrt{3}}{2}$  

•  $-\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$  

Multiple Choice

Evaluate cos(11π/6)

•  $-\frac{\sqrt{2}}{2}$  

•  $\frac{\sqrt{2}}{2}$  

•  $-\frac{\sqrt{3}}{2}$  

•  $-\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$  

Evaluating Sine

• sin(θ) = y-coordinate of the point associated with that angle

• sin(4π/3) = -√3/2

• sin(0) = 0

• sin(135°) = √2/2

Multiple Choice

Evaluate sin(60°)

• 0

•  $\frac{1}{2}$  
  

•  $\frac{\sqrt{2}}{2}$  
  

•  $\frac{\sqrt{3}}{2}$  

• 1

Multiple Choice

sin(7π/6)

• - ½

• √3 /2

• ½

• -√3 /2

• -√2 /2

Multiple Choice

sin 180°

• 1

• -1

• 0

• $-\frac{\sqrt{3}}{2}$

• $\frac{1}{2}$