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

Question

asked Dec 24, 2020 126k views

1 Answer

Vishal Dasadiya · Answer 1 · 2020-12-30T18:38:34+0000

Answer:

- 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:

$cos180^(\circ) = 0$