Question

sin(-pi)+cos(5pi)
Find the exact value

Answer 1

\(\large\color{black}{ \displaystyle \sin(-\pi)~~\Rightarrow~~-\sin(\pi)}\)
Do yo know what \(\large\color{black}{ \displaystyle \sin(\pi)}\) is ?

Answer 2

adding (or subtracting) 2pi inside these trig functions takes you once around the unit circle and back to the same point.

sin (-pi) = sin(pi) = 0
cos (5pi) = cos (3pi) = cos (pi) =-1

Answer 3

sin(-A)=-sin(A)
cos(-A)=cos(A)

Answer 4

it is -sin(pi)
which is technically the same thing, but just not to apply the rules for sines of other values

Answer 5

And then
\(\normalsize\color{black}{ \displaystyle \cos(5\pi)~~\Rightarrow~~\cos(4\pi+\pi)~~\Rightarrow~~\cos(4\pi)\cos(\pi)-\sin(4\pi)\sin(\pi) }\)

sin(pi) and cos(pi) should be the values you are familiar with.

Answer 6

I think I get it

Answer 7

that is cooL:)