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° = -\frac{\sqrt{2}}{2}
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
b. the function value is undefined.
select the correct choice below and fill in any answer boxes within your choice.
a. cos 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 cosine function formula for angles in the third quadrant

We know that \(\cos\theta=-\cos\theta_{r}\) (since cosine is negative in the third quadrant). And \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\)

So, \(\cos225^{\circ}=-\cos45^{\circ}\)

$$ \cos225^{\circ}=-\frac{\sqrt{2}}{2} $$

Answer:

\(\cos225^{\circ}=-\frac{\sqrt{2}}{2}\)