# Trigonometric

• Jun 11th 2013, 07:14 AM
Trefoil2727
Trigonometric
Given that sin20=x, cos10=y, state each of the following in terms of x and y
a) cos30
b) cos 5
• Jun 11th 2013, 08:18 AM
Plato
Re: Trigonometric
Quote:

Originally Posted by Trefoil2727
Given that sin20=x, cos10=y, state each of the following in terms of x and y
a) cos30
b) cos 5

a) $\displaystyle \cos(30^o)=\cos(10^o+20^o)$

b) $\displaystyle \cos(5^o)=\cos\left(\frac{10^o}{2}\right)$.

Now you show some work on your part.
• Jun 12th 2013, 06:14 PM
jpritch422
Re: Trigonometric
This is part a:

There is the identity $\displaystyle \cos(\theta + \phi) = \cos{\theta}\cos{\phi} - \sin{\theta}\sin{\phi}$

let $\displaystyle \space$ $\displaystyle \sin{\theta} = \sin{20^{\circ}} = x$ $\displaystyle \space$ and $\displaystyle \space$ $\displaystyle \cos{\phi} = \cos{10^{\circ}} = y$

that makes $\displaystyle \space$ $\displaystyle \cos{20^{\circ} = \sqrt{1 - x^2}$ $\displaystyle \space$ and $\displaystyle \space$ $\displaystyle \sin{10^{\circ} = \sqrt{1 - y^2}$

where $\displaystyle \space$ $\displaystyle \theta = 20^{\circ}$ $\displaystyle \space$ $\displaystyle \phi = 10^{\circ}$