10.4 CA – Inverse Trig Functions
Pre-Calculus
For 1-6, graph the function.
1) 𝑦 = 3 sin−1 𝑥
4) 𝑦 = 2 sin−1 𝑥 + 𝜋
Name: _____________________________
2) 𝑦 = cos−1 (𝑥 − 2)
5) 𝑦 = 3 cos−1 𝑥 −
3) 𝑦 = tan−1 𝑥 +
𝜋
𝜋
2
6) 𝑦 = 2tan−1 𝑥 − 𝜋
2
For 7-14 , find the exact value of the expression. Do not use a calculator! (radians or degrees both work)
7) sin (arccsc (
2√ 3
3
))
√3
3
11) sec (arctan ( ))
√2
2
8) cos (arcsin ( ))
√3
2
12) sin (arcsin ( ))
1
√2
2
9) cos (arccos ( ))
10) tan (arcsin ( ))
13) cos(arcsec(2))
14) csc(arctan(√3))
2
For 15-22, find the approximate value of the expression by using a calculator. Round to three decimals. Only
one answer is necessary. Assume degrees for inverse functions.
3
21
1
16) sec(56° )
15) sin−1 ( )
17) arcsec ( )
18) sec ( )
4
20
5
7
3
22) sec −1 (5)
21) arccsc(2.1)
7
20) cot−1 ( )
19) cot ( )
3
For 23-26 , use a reference triangle to find the exact value of the expression.
4
7
23) tan (sin−1 ( ))
5
11
3
25) csc (cot−1 ( ))
24) sec (arccsc ( ))
2
26) sec (sin−1 ( ))
6
7
y
Answers to 10.4 Corrective Assignment
y
1)

2)

3)










x
x

y










x








y


5)



y
4)

6)

y










x






x







x












7)
√3
2
11)

8)

√2
2
2√ 3
3 

12)
9)

√3
2
4
√105
=
4√105
105
24)
7
√45
=
7
3√ 5
10) 1
2
13)
15) 48.59°
16) 1.788
19) −0.955 (use radians!) 20) 23.199°
23)
1
1
2
17) 17.753
21) 28.437°
=
7√ 5
15
25)
√61
6
14)
2√ 3
3
18) 1.02 (use radians!)
22) 78.463°
26)
7
2√10
=
7√10
20