Question

What is Cos(225)°?

Answer 1

The exact value of cos(225°) is √2/2.
the following are the steps to calculate the value of cos (225°).
225=180+45
cos(x+y)=cos (x)×cos(y)-sin(x)×sin(y)
since 225°= 180°, we can use our angle sum identity to rewrite cos 225°in terms of sine and cosine of 180° and 45° as follows.
cos(225°)=cos(180°+45°)=cos(180°)×cos(45°)-sin(180°)×sin(45°)
Now we know the values of all angles
1. Cos(180°)= -1
2.cos (45°)= √2/2
3. Sin (180°)= 0
4. Sin (45°)= √2/2
substituting the all values in the above equation we get
cos (225°)=cos(180°)×(cos45°)-sin(180°)×sin(45°)
= [(-1)×√2/2]-[0×√2/2]
= -√2/2