Evaluate: cot -15π/4
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0
Answer:
✌ cot
(
−
π
6
)
=
−
√
3
Explanation:
We will use the following:
(1)
cot
(
x
)
=
cos
(
x
)
sin
(
x
)
(2)
sin
(
−
x
)
=
−
sin
(
x
)
(3)
cos
(
−
x
)
=
cos
(
x
)
(4)
cos
(
π
6
)
=
√
3
2
(5)
sin
(
π
6
)
=
1
2
Verification of these facts is a good exercise, and may be done using basic definitions together with the unit circle for 1-3.
For 4 and 5, as a hint, bisect an equilateral triangle with side length
1
into two equal right triangles. What are the angles of the right triangles?
With this, we have
cot
(
−
π
6
)
=
cos
(
−
π
6
)
sin
(
−
π
6
)
(by 1)
⇒
cot
(
−
π
6
)
=
cos
(
π
6
)
−
sin
(
π
6
)
(by 2 and 3)
⇒
cot
(
−
π
6
)
=
−
√
3
2
1
2
=
−
√
3
(by 4 and 5)
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