Question

find the exact values of the six trigonometric functions of the given angle do not use a calculator
225°
select the correct choice below and fill in any answer boxes within your choice
a. sin 225° =
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression )
b. the function value is undefined

Explanation:

Step1: Determine the reference angle

The angle \(225^{\circ}\) is in the third quadrant. The reference angle \(\theta_{r}=225^{\circ}- 180^{\circ}=45^{\circ}\).

Step2: Use the sign of the trigonometric function in the third quadrant

For the sine function, \(\sin\theta =-\sin\theta_{r}\) (since sine is negative in the third quadrant).
We know that \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\), so \(\sin225^{\circ}=-\sin45^{\circ}\).

Answer:

\(-\frac{\sqrt{2}}{2}\)