Warmup
Find the value of each of the following
without a calculator.
1. sin 2π
3
3. tan (-360o)
2. sec 5π
4
4. csc 17π
2
1
Inverse Trig Functions (4.7)
y = sin x
Question: Do all
functions have inverses?
y = arcsin x = sin­1 x
2
y = cos x
y = arccos x = cos­1 x
3
Inverse Trig Functions
Inverse Sine
y = arcsin x or y = sin-1 x
Domain : -1 ≤ x ≤ 1
Range : - π/2 ≤ y ≤ π/2
Inverse Cosine
y = arccos x or y = cos-1 x
Domain : -1 ≤ x ≤ 1
Range: 0 ≤ y ≤π
Inverse Tangent
y = arctan x or y = tan-1 x
Domain: - ∞ < x < ∞
Range: - π/2 < y < π/2
4
Inverse sine function:
Remember:
y = arcsin x or y = sin­1 x
Domain : ­1 ≤ x ≤ 1
Range : ­ π/2 ≤ y ≤ π/2
"the arcsine of x is the angle (or number) whose sine is x"
1. y = sin-1 -1
2
"the angle whose sine is -1/2"
2. y = arcsin (0)
3. y = sin-1(-1)
4. y = arcsin(2)
5
Inverse Cosine
Remember: y = arccos x or y = cos-1 x
Domain : -1 ≤ x ≤ 1
Range: 0 ≤ y ≤π 1. y = arccos(-1)
2. y = cos-1 _1_
√2
3. y = arccos - √3
2
4. y = arccos -1
√2
5. y = sec-1(2)
6
Inverse Tangent
Remember: y = arctan x or y = tan-1 x
Domain: - ∞ < x < ∞
Range: - π/2 < y < π/2
1. y = tan-1(-1)
2. y = arctan 1_
√3
3. y = arctan (-√3)
7
1. y = arcsin(sin (-π/2))
2. y = arccos(cos(-π/3))
3. y = tan(arccos(-1/2))
y = arcsin x
Domain : -1 ≤ x ≤ 1
Range :- π/2 ≤ y ≤ π/2
y = arccos x
Domain : -1 ≤ x ≤ 1
Range: 0 ≤ y ≤π y = arctan x
Domain: - ∞ < x < ∞
Range: - π/2 < y < π/2
8
4. y = sin(cos-1(-1/2))
5. y = arcsin(sin(3π/2))
6. y = arcsin(sin 5π/3)
y = arcsin x
Domain : -1 ≤ x ≤ 1
Range :- π/2 ≤ y ≤ π/2
y = arccos x
Domain : -1 ≤ x ≤ 1
Range: 0 ≤ y ≤π y = arctan x
Domain: - ∞ < x < ∞
Range: - π/2 < y < π/2
7. y = tan(arctan (14))
8. y= cos(arccos π)
9
Use a calculator to evaluate the following.
Answers need to be in radians. Round your answer
to two decimal places.
1. arcsin .98
2. arctan 13
3. arccos 14
10
Homework
Pg 351
#6-21 mult. of 3,
27-36 mult. of 3
*Finish Test Corrections*
11
12