finD the exact value of the expression cos 225 Degree-cos 45 Degree

Question

ipwnbunnies · Answer

Let's look at cos 225 degrees: It exist in the third quadrant, where cosine is negative, so we'll know this # will be negative. 225 degrees is similar to 45 degree angle b/c (225-180) = 45. So you can look at cos 225 as -cos 45.

ipwnbunnies · Answer

So now, we'll have -cos 45 - cos45, simplifies to -2cos 45. Do you know the 45-45-90 special triangle?

anonymous · Answer

3-4-5

ipwnbunnies · Answer

No.

ipwnbunnies · Answer

cosine of an angle is adjacent side/hypotenuse. So the answer is -2*(adjacent/hypotenuse).

anonymous · Answer

but the answer is wrong

anonymous · Answer

it suppose to be -1.4142

ipwnbunnies · Answer

That's what I'm getting.

ipwnbunnies · Answer

cos 45 is 1/sqrt(2) = sqrt(2)/2

-2*sqrt(2)/2 = -sqrt(2) = -1.414

anonymous · Answer

but how Do i get the fraction ?

ipwnbunnies · Answer

$$-2*\frac{ \sqrt{2} }{ 2 }$$

anonymous · Answer

thank you so much i got it now...

ipwnbunnies · Answer

To make it a bit more expanded for your original question. cos 225 - cos45, as I said, it can be rewritten as -cos45 - cos45. 

$$\frac{ -\sqrt{2} }{ 2 } - \frac{ \sqrt{2} }{ 2 }$$

ipwnbunnies · Answer

Great