Answer:
[tex]cos(-2835^{\circ}) = \frac{1}{\sqrt{2}}[/tex]
[tex]sin(-2835^{\circ}) = \frac{1}{\sqrt{2}}[/tex]
Solution:
As per the question:
We need to find the values of:
[tex]cos(-2835^{\circ})[/tex]
[tex]sin(-2835^{\circ})[/tex]
Now, we know that:
[tex]cos(- \theta) = cos\theta[/tex]
[tex]sin(- \theta) = - sin\theta[/tex]
Also
[tex]cos(2n\pi - \theta) = cos\theta[/tex]
[tex]sin(2n\pi - \theta) = - sin\theta[/tex]
Now,
From the above eqn (1) and (2):
[tex]cos(-2835^{\circ}) = cos(2835^{\circ})[/tex]
[tex]sin(-2835^{\circ}) = - sin(2835^{\circ})[/tex]
Now the above respective values can be further calculated from eqns (3) and (4):
[tex]cos(2(8)\pi - 45^{\circ}) = cos(45^{\circ}) = \frac{1}{\sqrt{2}}[/tex]
[tex]sin(2(8)\pi - 45^{\circ}) = -(- sin(45^{\circ})) = \frac{1}{\sqrt{2}}[/tex]
where
n = 8
