Inverse Trig Functions

1. Inverse Trig Functions

2. Inverses • How do we know if something has an inverse? • Vertical line tests tell us if something is a function • Horizontal line tests will tell us if there is an inverse. • Do any of the 6 trig functions have inverses? • What if we restricted what we were looking at…

3. Inverse Sine Function “Arcsine Function”

4. Evaluate without a Calculator You can only have answers between [-π/2, π/2] • sin-1(1/2) • sin-1(-√3/2)

5. Evaluate without a Calculator You can only have answers between [-π/2, π/2] • sin-1(π/2) • sin-1(sin(π/9)) • sin-1(sin(5π/6))

6. Evaluate with a Calculator Use the “2nd” button and the “sin” button. • sin-1(-.081) • sin-1(sin(3.49π)) • sin-1(3)

7. Inverse Cosine Function

8. Evaluate without a Calculator • cos-1(-√2/2) • cos-1(cos(-1.1))

9. Inverse Tangent Function

10. Evaluate without a Calculator • tan-1(√3) • tan-1(-1)

11. Evaluate with a Calculator • sin-1(0.362) in degrees • tan-1(-12.5) in degrees • tan-1(2.37) in radians • sin-1(-0.46) in radians

12. Evaluate without a Calculator • cos(sin-1(1/2)) • sin-1(cos(π/4)) • arcsin(cos(π/3)) • cos(tan-1(√3))