Question

Find the exact value.
cos225°

Answer 1

Exact form: -square root 2/2 (I don't have a square root symbol)
Decimal form: -0.70710678

Answer 2

`cos(225$^(\circ)$) = -√(2) /2 \approx-0.707`

Explanation:

We can use the next table which show you the simplest algebraic values of trigonometric functions. As you can see:

`cos(45)=(√(2))/(2)`

And actually:

`cos(45+n90)=\pm(√(2) )/(2) \hspace{3}n\in Z`

As you can see it can be positive or negative, it depends on the quadrant. You maynotice that the cosine function is positive in the first quadrant and the fourth quadrant, and negative in the second quadrant and the third quadrant. 225 is a multiple of 45, (45+2*90=45+180=225) also 225 is in the third quadrant. So:

`cos(45+180)=cos(225)=-(√(2) )/(2) \approx -0.707`