# Prove sin and cos = 0

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• Nov 1st 2009, 07:14 PM
Joel
Prove sin and cos = 0
Hi all,

sin330cos150 - cos390sin390 = 0

Prove:

What am I to do with this? Do I convert ll to the one function or......mmmm got nothing.

Any help would be appreciated.
• Nov 1st 2009, 08:33 PM
adkinsjr
Quote:

Originally Posted by Joel
Hi all,

sin330cos150 - cos390sin390 = 0

Prove:

What am I to do with this? Do I convert ll to the one function or......mmmm got nothing.

Any help would be appreciated.

Remember that the trig functions are periodic.

$\displaystyle cos(390)=cos(30)=\frac{\sqrt{3}}{2}$

$\displaystyle sin(390)=sin(30)=\frac{1}{2}$

The other two values are:

$\displaystyle sin(330)=-\frac{1}{2}$

$\displaystyle cos(150)=-\frac{\sqrt{3}}{2}$

If you don't see why these are true, look here: Trigonometric functions - Wikipedia, the free encyclopedia

Scroll down and look at the unit circle next to the paragraph "Unit-circle definitions"
• Nov 2nd 2009, 03:15 AM
Joel
so it would now look like....

sin330cos150 - cos390sin390 = 0

(- ½)(-√3/2) - ( ½)(√3/2) = 0
√3/2 / 2 - √3/2 / 2 = 0 which is true

Is this how i should set it out ?
• Nov 2nd 2009, 10:59 AM
adkinsjr
(Yes)(Yes)

Yup