Precalculus: Chapter 4
Graphing Sine and Cosine
1. y = sin x
−2π
−3π/2
−π
2. y = cos x
4.0
4.0
3.0
3.0
2.0
2.0
1.0
1.0
−π/2
π/2
π
3π/2
2π
−3π/2
−π
−3π/2
−π
−π
−π/2
−2.0
−2.0
−3.0
−3.0
−4.0
−4.0
π/2
π
3π/2
2π
π/2
π
3π/2
2π
⎛ π⎞
4. y = −4sin ⎜ x − ⎟
2⎠
⎝
4.0
4.0
3.0
3.0
2.0
2.0
1.0
1.0
−π/2
π/2
π
3π/2
2π
−2π
−3π/2
−π
−π/2
−1.0
−1.0
−2.0
−2.0
−3.0
−3.0
−4.0
−4.0
⎛ π⎞
5. y = 2cos ⎜ x − ⎟
4⎠
⎝
−2π
−3π/2
−1.0
3. y = 3cos x +1
−2π
−2π
−1.0
⎛ π⎞
6. y = −2sin ⎜ x + ⎟ +1
4⎠
⎝
4.0
4.0
3.0
3.0
2.0
2.0
1.0
1.0
−π/2
π/2
π
3π/2
2π
−2π
−3π/2
−π
−π/2
π/2
−1.0
−1.0
−2.0
−2.0
−3.0
−3.0
−4.0
−4.0
π
3π/2
2π
⎛ π⎞
7. y = sin ⎜ x − ⎟
4⎠
⎝
−2π
−3π/2
−π
⎛ π⎞
8. y = cos ⎜ x + ⎟
2⎠
⎝
4.0
4.0
3.0
3.0
2.0
2.0
1.0
1.0
−π/2
π/2
π
3π/2
2π
−3π/2
−π
−3π/2
−π
−π
−π/2
π/2
−2.0
−2.0
−3.0
−3.0
−4.0
−4.0
π
3π/2
2π
⎛ π⎞
10. y = cos ⎜ x − ⎟ + 2
4⎠
⎝
4.0
4.0
3.0
3.0
2.0
2.0
1.0
1.0
−π/2
π/2
π
3π/2
2π
−2π
−3π/2
−π
−π/2
−1.0
−1.0
−2.0
−2.0
−3.0
−3.0
−4.0
−4.0
4.0
4.0
3.0
3.0
2.0
2.0
1.0
1.0
−π/2
π/2
π
3π/2
2π
π/2
π
3π/2
2π
⎛ π⎞
12. y = 2sin ⎜ x + ⎟ +1
2⎠
⎝
11. y = 3cos ( x + π )
−2π
−3π/2
−1.0
9. y = 2sin x −1
−2π
−2π
−1.0
π/2
π
3π/2
2π
−2π
−3π/2
−π
−π/2
−1.0
−1.0
−2.0
−2.0
−3.0
−3.0
−4.0
−4.0