04/19/23 Perkins

AP Calculus AB

Day 1Section 5.6

Inverse Trig Functions

1siny xsiny x

• To have an inverse, a function must be 1-to-1.• Since sine and cosine are not, we must limit their domains.

2 3

2 2

1

1

siny x

2 2

32 2

1

1

cosy x

2

QI

QI

QIV

QII

1cosy xcosy x

1sin QI 1sin QIV

1cos QI 1cos QII

More Inverse Trig Functions

1cot y x

4

2 3

4

1

1

4

2 3

4

1

1

1tany x

4

2

1csc QI 1csc QIV

1sec QI 1sec QII

1cot QI 1cot QII

1cscy xThe quadrants for csc are the same as sin.

The quadrants for sec are the same as cos.

1secy x

The quadrants for cot are different than tan.

1tan QI 1tan QIV

Solve.1

1. arcsin2

y 32. arccos

2

33. sin arctan

4

1sin

2y

6ref

sin QI

6y

3cos

2x

x

6ref

cos QII

5

6x

3arctan

4

x

sin x

3tan

4

3

4

5

oppx

hyp

3

5x

tan QI

QI

Solve.

5. sec arctan 3x

54. tan arcsin

6

5

11

6

5arcsin

6

5

sin6

sin QIV

tan x 5

11x

QIV

arctan 3x

tan 3x

sec x

3x

1

29 1x

29 1

1

xx

Write in algebraic form.

2366. arcsin arccos

6

xy

236 x

x

6

236

cos arcsin6

xy

236

arcsin6

x

236sin

6

x

cos y

6

xy

Write in algebraic form.

Perkins

AP Calculus AB

Day 1Section 5.6

cosy x

2 3

2 2

1

1

2

Inverse Trig Functions

1siny x

siny x

2 3

2 2

1

1

2

1cosy x

More Inverse Trig Functions

1cot y x

4

2 3

4

1

1

1tany x

4

2 3

4

1

1

4

2

1cscy x 1secy x

Solve.1

1. arcsin2

y 32. arccos

2

33. sin arctan

4

Solve.

5. sec arctan 3x

54. tan arcsin

6

Write in algebraic form.

2366. arcsin arccos

6

xy

Write in algebraic form.