Unit Circle

What is the length of the hypotenuse of the triangle? (Think about it as a radius)

OP= (a)  

Label OP on your paper.

Using θ as a reference angle, mark the triangle sides as Opp, Adj, and Hyp.

Label these on the triangle on your paper.

• Hyp

• x

• Adj

• OP

• Opp

• y

• sinθ

• OP

• 1

• cosθ

What about tangent? Use the triangle to answer the following questions.

In terms of x and y, what does tanθ equal?

tanθ=​ ​ (a)  

In terms of sinθ and cosθ, what does tanθ equal?

tanθ=​ (b)  

• x
• y
• sinθ
• cosθ

Unlike right triangle trigonometry, sine and cosine may be negative.

Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:

sine is positive: ​ (a)   ​& (b)  

sine is negative: ​ ​ (c)   &​ (d)  

• I
• II
• III
• IV

Unlike right triangle trigonometry, sine and cosine may be negative.

Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:

cosine is positive: ​ (a)   ​& (b)  

cosine is negative: ​ ​ (c)   &​ (d)  

• I
• IV
• II
• III

Unlike right triangle trigonometry, sine and cosine may be negative.

Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:

tangent is positive: ​ (a)   ​& (b)  

tangent is negative: ​ ​ (c)   &​ (d)   ​

• I
• III
• II
• IV

• 0
• 1
• -1