Trig Inverses
Find the values of 𝑥 in the interval 0 ≤ 𝑥 < 360 that satisfy each equation.
_________________________ 1.
𝑥 = cos−1 0
_________________________ 2.
𝑥 = sin−1 ( 2)
_________________________ 3.
𝑥 = arctan
_________________________ 4.
𝑥 = sec −1 2
_________________________ 5.
arctan 0 = 𝑥
_________________________ 6.
arcsin = 𝑥
1
√
√3
3
1
2
Evaluate each expression. Find all possible values.
_________________________ 7.
cos−1 0
_________________________ 8.
sin−1(−1)
_________________________ 9.
sin−1 1
_________________________ 10.
cos−1(−1)
_________________________ 11.
tan−1
_________________________ 12.
arccos (− 2)
_________________________ 13.
arcsin (−
_________________________ 14.
arcsin (− )
_________________________ 15.
arccos ( 2 )
_________________________ 16.
arctan √3
_________________________ 17.
tan−1 (−1)
√3
3
1
√3
)
2
1
2
√2
Evaluate each expression. Assume that all angles are in Quadrant I.
1
2
_________________________ 18.
sin (sin−1 )
_________________________ 19.
tan(tan−1 4)
_________________________ 20.
cot (arctan 5)
_________________________ 21.
sin (cos −1
_________________________ 22.
sec (cos−1 2)
_________________________ 23.
cos (arccot )
_________________________ 24.
tan (sin−1 17)
_________________________ 25.
sin(tan−1 1)
4
√3
)
2
1
4
3
15
Evaluate each expression. Find all possible values.
1
_________________________ 26.
sin (sin−1 2)
_________________________ 27.
sin (cos −1
_________________________ 28.
sin(tan−1 1)
√3
)
2
Trig Inverses KEY
Find the values of 𝑥 in the interval 0 ≤ 𝑥 < 360° that satisfy each equation.
90°,
270°
_________________________
1.
𝑥 = cos−1 0
45°,
135°
_________________________
2.
𝑥 = sin−1 ( ) What angle has a sine of
30°,
210°
_________________________
3.
𝑥 = arctan
60°,
300°
_________________________
4.
𝑥 = sec −1 2
What angle has a cosine of 2?
0°,
180°
_________________________
5.
arctan 0 = 𝑥
What angle has a tangent of 0?
30°,
150°
_________________________
6.
arcsin = 𝑥
1
√2
√2
?
2
√3
3
What angle has a tangent of
1
2
Evaluate each expression. Find all possible values.
90° ± 180𝑛
_________________________
7.
cos−1 0
270° ± 360𝑛
_________________________
8.
sin−1(−1)
90° ± 360𝑛
_________________________
9.
sin−1 1
180° ± 360𝑛
_________________________
10.
cos−1(−1)
30° ± 180𝑛
_________________________
11.
tan−1
120° ± 360𝑛, 240° ± 360𝑛 12.
_________________________
arccos (− 2)
240° ± 360𝑛, 300° ± 360𝑛 13.
_________________________
arcsin (−
210° ± 360𝑛, 330° ± 360𝑛 14.
_________________________
arcsin (− )
45° ± 360𝑛, 315° ± 360𝑛 15.
_________________________
arccos ( 2 )
60° ± 180𝑛
_________________________
16.
arctan √3
135° ± 180𝑛
_________________________
17.
tan−1 (−1)
√3
3
1
√3
)
2
1
2
√2
What angle has a cosine of 0?
√3
?
3
1
1
2
What angle has a sine of ?
Evaluate each expression. Assume that all angles are in Quadrant I.
1
1
1
2
_________________________
18.
sin (sin−1 ) What is the sine of an angle that has a sine of ?
2
2
4
_________________________
19.
tan(tan−1 4)
What is the tangent of an angle that has a tangent of 4?
5
4
_________________________
20.
cot (arctan 5) What is the cotanent of an angle that has a tangent of 5?
4
4
1
2
_________________________
21.
sin (cos −1
2
_________________________
22.
sec (cos−1 2)
4
5
_________________________
23.
cos (arccot ) What is the cosine of an angle that has a cotangent of ? 5
3
3
15
8
_________________________
24.
√2
2
_________________________
25.
√3
)
2
1
What is the sine of an angle that has a cosine of
√3
?
2
1
What is the secant of an angle that has a cosine of 2?
4
4
3
4
15
tan (sin−1 )
17
What is the tangent of an angle that has a sine
15
of ?
17
17
8
sin(tan−1 1)
Evaluate each expression. Find all possible values.
1
2
_________________________
26.
sin (sin−1 2)
1
±
2
_________________________
27.
sin (cos −1
√2
±
2
_________________________
28.
sin(tan−1 1)
1
√3
)
2
What is the sine of an angle that has a tangent of 1?
15