Question

Consider an angle with a measure of θ=225∘.

Sketch a diagram representing the situation.

Determine the measure of the reference angle for this angle.
 _______°   

Now, determine the exact values of the following expressions. Your answers should include fractions and square roots, and not decimal values.

cos(θ)=

sin(θ)=

tan(θ)=

​

Answer 1

cos 225° =
`-(√(2) )/(2)`

sin 225° =
`-(√(2) )/(2)`

tan 225° = 1

Explanation:

I cannot sketch a diagram, but a 225° angle is a 3rd quadrant angle and the reference angle is 45° (225 - 180 = 45)

cos and sin are negative in the 3rd quadrant and the tan is positive

cos 225° = - cos 45° =
`-(√(2) )/(2)`

sin 225° = -sin 45° =
`-(√(2) )/(2)`

tan 225° = tan 45° = 1