1. Getting ready for Pre-Calculus class.

2. From Geometry:
Special triangles

4. π/2 𝜋/3 60° 𝜋 3 𝜋/4 45° 𝜋/6 𝜋 4 30° 𝜋 6 2𝜋/3 3𝜋/4 𝜋 5𝜋/6 𝜋 2𝜋 7𝜋/6
Angle/degrees
Angle/radians
 sin
cos
 tan
cot 0 
30 
45 
60 
90 
120 
135 
150
 180
210 
225 
240 
 270
 300
 315
330 
360 
𝜋/3
60°
𝜋 3
  𝜋 2
𝜋/4
90 
45°
𝜋 4
𝜋/6
π/2
30°
𝜋 6
2𝜋/3
3𝜋/4 𝜋 
180
5𝜋/6 0  𝜋  2𝜋
360
7𝜋/6
5𝜋/4
4𝜋/3
3𝜋/2 
3𝜋 2  
 270
5𝜋/3
7𝜋/4
11𝜋/6 2𝜋

5. 𝑦= sin 𝑥 =𝑜𝑝𝑝/ℎ𝑦𝑝
𝑦= cos 𝑥 =𝑎𝑑𝑗/ℎ𝑦𝑝
𝑦= tan 𝑥 = sin 𝑥 cos 𝑥 =𝑜𝑝𝑝/𝑎𝑑𝑗
𝑦= cot 𝑥 = cos 𝑥 sin 𝑥 =𝑎𝑑𝑗/𝑜𝑝𝑝

6. One more time
1 2
2 2
3 2 1
3 2
2 2
1 2 1
1 3 3 1
1 3 1 3

7. θ 𝜋 2 𝜋 3𝜋 2 2𝜋 𝑦=sin⁡(𝑥) 𝜋 2 𝑦=𝑠𝑖𝑛𝑥 𝜋 2𝜋 3𝜋 2 sin 3𝜋 2 =−1 sin 𝜋 2 =12𝜋
3𝜋 2 θ
𝜋 2 𝜋
3𝜋 2 2𝜋
𝑦=sin⁡(𝑥)
sin 3𝜋 2 =−1
sin 𝜋 2 =1
sin 0 =0
sin 𝜋 =0
sin 2𝜋 =0

8. θ 𝜋 2 𝜋 3𝜋 2 2𝜋 𝑦=cos⁡(𝑥) 𝜋 2 𝑦=cos⁡(𝑥) 𝜋 2𝜋 3𝜋 2 cos 𝜋 2 =02𝜋
3𝜋 2 θ
𝜋 2 𝜋
3𝜋 2 2𝜋
𝑦=cos⁡(𝑥)
cos 𝜋 2 =0
cos 3𝜋 2 =0
cos 𝜋 =−1
cos 2𝜋 =1
cos 0 =1

9. 𝑦= sin⁡(𝜋/2) cos⁡(𝜋/2) = 1 0 =undefined
𝑦=tan⁡(𝑥)
𝜋 2
𝜋 4 𝜋 2𝜋
3𝜋 2
𝑦= tan 𝑥 = sin⁡(𝑥) cos⁡(𝑥)
𝑦= tan 𝑥 = sin⁡(0) cos⁡(0) = 0 1 =0
𝑦= sin⁡(3𝜋/2) cos⁡(3𝜋/2) = −1 0 =𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
𝑦= sin⁡(𝜋/4) cos⁡(𝜋/4) = 2 /2 2 /2 =1
𝑦= sin⁡(𝜋/2) cos⁡(𝜋/2) = 1 0 =undefined
𝑦= tan 𝑥 = sin⁡(𝜋) cos⁡(𝜋) = 0 1 =0

10. 𝑦=cot⁡(𝑥)
𝜋 2
3𝜋 4
𝜋 4 𝜋 2𝜋
3𝜋 2
𝑦= cot 𝑥 = cos⁡(𝑥) sin⁡(𝑥)
𝑦= cot 𝑥 = cos⁡(𝜋/2) sin⁡(𝜋/2) = 0 1 =0
𝑦= cot 𝑥 = cos⁡(𝜋/4) sin⁡(𝜋/4) = 2 /2 2 /2 =1
𝑦= cot 𝑥 = cos⁡(0) sin⁡(0) =𝑢𝑛𝑑𝑒𝑓
𝑦= cot 𝑥 = cos⁡(3𝜋/4) sin⁡(3𝜋/4) = 2 /2 2 /2 =−1
𝑦= cot 𝑥 = cos 𝜋 sin⁡(𝜋) =𝑢𝑛𝑑𝑒𝑓