Question

If theta = n ∙ 360 + 180, for some integer n, then cos(theta°) = _____, and sin(theta°) = ______.

Answer 1

- 1, 0

Solution:

As per the question:

`\theta = 360n + 180^(\circ)`

Now,

We know that:

`cos(2\pi n + \phi) = cos\phi`

Also,

`sin(2\pi n + \phi) = cos\phi`

In the question,
`\phi = 180^(\circ)`

Therefore, we can write:

`cos(360n + 180^(\circ)) = cos180^(\circ)`

We know that:

`cos180^(\circ) = - 1`

Similarly,

`sin(360n + 180^(\circ)) = sin180^(\circ)`

We know that:

`cos180^(\circ) = 0`