Thread: turning trigonomic functions into surds

how do i turn cos45 into a surd? or anyother function for that matter? In part of the equation below;

-2 x (x+2) x 4 x cos45

How do i find x?

Hello,

Originally Posted by Flexible

how do i turn cos45 into a surd? or anyother function for that matter? In part of the equation below;

-2 x (x+2) x 4 x cos45

How do i find x?

cos(45) is supposed to b a known value, that is sqrt(2)/2

this can be "proved" this way :
cos(45)=sin(45) (because cos(90-x)=sin(x))
we know that cos²(x)+sin²(x)=1
hence 2cos²(x)=1
cos²(x)=1/2
cos(x)=+ or - 1/sqrt(2)=+ or - sqrt(2)/2

since 45 is in the first quadrant, its cosine is positive. hence it's sqrt(2)/2