1. Warm-Up: Give the exact values of the following
Warm-Up: Give the exact values of the following! (If you must, use your unit circle.) -1
𝑠𝑖𝑛 7𝜋 2 =
𝑐𝑜𝑠− 𝜋 2 =
𝑠𝑖𝑛 7𝜋 4 =
𝑐𝑜𝑠− 5𝜋 3 =
Cos 300º =
Sin -540º =
Cos 405º =
Sin 3600º=
2 2

2. Other trig functions
Today we will use the exact values on the unit circle to evaluate other trig functions.

3. Remember to RATIONALIZE the denominator
tangent y x
𝑡𝑎𝑛𝜃= 𝑦 𝑥 or 𝑡𝑎𝑛𝜃= 𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃
Example
Tan 0 º = 0 1 =0
On the unit circle, what angle measurements would cause tan(ө) to be undefined? You must explain your answer.
Recall
𝑐𝑜𝑠𝜃= 𝑥 𝑟
𝑠𝑖𝑛𝜃= 𝑦 𝑟
tan 𝜋 6 =
= 1 2 ∙ =
Remember to RATIONALIZE the denominator
∙ =

4. You try Evaluate the following
You try Evaluate the following. Give exact values and rationalize all denominators
𝑡𝑎𝑛 5𝜋 3 =
𝑡𝑎𝑛 3𝜋 4 =
𝑡𝑎𝑛− 𝜋 6 =
tan -300º =
tan -540º =
tan 405º =
− 3 3 -1 − 1

5. In other words, cotangent is the reciprocal of the tangent function!y x
𝑐𝑜𝑡𝜃= 𝑥 𝑦 or 𝑐𝑜𝑡𝜃= 𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃
Example
cot 270 º = 0 −1 =0
On the unit circle, what angle measurements would cause cot(ө) to be undefined? You must explain your answer.
In other words, cotangent is the reciprocal of the tangent function!
cot 𝜋 6 =
= ∙ 2 1 = 3

6. -1 -1 undefined 𝑐𝑜𝑡 4𝜋 3 = 𝑐𝑜𝑡− 3𝜋 4 = 𝑐𝑜𝑡 11𝜋 6 = − 3
You try Evaluate the following. Give exact values and rationalize all denominators
𝑐𝑜𝑡 4𝜋 3 =
𝑐𝑜𝑡− 3𝜋 4 =
𝑐𝑜𝑡 11𝜋 6 =
3 3
cot -270º =
cot 135º =
cot3600º = -1 -1
− 3
undefined

7. r y x Secant and cosecant 𝑐𝑠𝑐𝜃= 𝑟 𝑦 = 1 𝑦 = 1 𝑠𝑖𝑛𝜃 1 − 3 2 = 2 − 3
𝑐𝑠𝑐𝜃= 𝑟 𝑦 = 1 𝑦 = 1 𝑠𝑖𝑛𝜃
In other words, cosecant is the reciprocal of sine
Example: csc(− 2𝜋 3 )
1 − = 2 − 3
Don’t forget to rationalize the denominator!
2 − 3 ∙ =−
𝑠𝑒𝑐𝜃= 𝑟 𝑥 = 1 𝑥 = 1 𝑐𝑜𝑠𝜃
In other words, secant is the reciprocal of cosine
Example: sec(− 𝜋 4 ) =
Don’t forget to rationalize the denominator!
∙ = = 2

8. You try Evaluate the following
You try Evaluate the following. Give exact values and rationalize all denominators
𝑠𝑒𝑐 7𝜋 2 =
𝑠𝑒𝑐8𝜋 =
𝑠𝑒𝑐 7𝜋 4 =
undefined
𝑐𝑠𝑐 7𝜋 3 =
⁡𝑐𝑠𝑐(− 3𝜋 2 ) =
𝑐𝑠𝑐 3𝜋 4 = 1 1 2 2

9. Closure
On the unit circle, what angle measurements would cause sec(ө) to be undefined? You must explain your answer.
On the unit circle, what angle measurements would cause csc(ө) to be undefined? You must explain your answer.