Inverse Trigonometric Functions Worksheets With Answers Page 4
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24INVERSE TRIGONOMETRIC FUNCTIONS
21
3
3
= θ , then cos θ =
If cos
.
–1
2
Solution
2
3
Since we are considering principal branch, θ ∈ [0, π]. Also, since
> 0, θ being in
2
3
π
the first quadrant, hence cos
=
.
–1
2
6
–π
sin
Evaluate tan
.
–1
Example 2
2
⎛
⎞
⎛ ⎞
–π
π
π
−
sin
sin
−
⎜
⎜ ⎟
⎟
tan
= tan
= tan
(–1) =
.
–1
–1
–1
Solution
2
⎝ ⎠
2
⎝
⎠
4
13π
cos
Find the value of cos
.
–1
Example 3
6
π
13π
⎛
⎞
⎛
⎞
π
π +
–1
cos
cos (2
)
cos
cos
⎜
⎟
=
⎜
⎟
cos
= cos
–1
–1
Solution
6
⎝
6
⎠
⎝
6
⎠
π
=
.
6
9π
tan
.
Find the value of tan
–1
Example 4
8
π
⎛
⎞
9π
π +
tan
= tan
⎜
⎟
tan
tan
–1
–1
Solution
8
⎝
8
⎠
⎛
π
⎞
⎛ ⎞
π
–1
tan
tan
⎜
⎜ ⎟
⎟
=
=
8
⎝ ⎠
⎝
⎠
8
Evaluate tan (tan
(– 4)).
–1
Example 5
x ∈ R, tan (tan
Since tan (tan
x) = x,
(– 4) = – 4.
–1
∀
–1
Solution
Evaluate: tan
–1
– sec
–1
(–2) .
3
Example 6
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