Question

2. Evaluate the following Trigonometric Functions and give the exact value.A. sin pi/6B. cos 225*

Answer 1

Let's evaluate the given Trigonometric functions and find the exact value.

Question A:

`\begin{gathered} \sin (\pi)/(6) \\ \\ Exact\text{ value of }\sin \text{ }(\pi)/(6)=(1)/(2) \\ \\ \text{Thus, we have:} \\ \sin (\pi)/(6)=(1)/(2)=0.5 \\ \\ \sin (\pi)/(6)=0.5 \end{gathered}`

Question B:

cos 225°

To find the exact value of cos 225°, apply the reference angle by finding the angle in the first quadrant with equivalent values.

Thus, we have:

225 - 90 - 90 = 45°

Make the expression negative because cosine is negative in the third quadrant.

We have:

`\begin{gathered} -\cos 45\degree \\ \\ \text{The exact value of cos45}\degree\text{ is }\frac{\sqrt[]{2}}{2} \\ \\ -\cos 225\degree=-\frac{\sqrt[]{2}}{2}=-0.707 \\ \\ -\cos 225\degree=-0.707 \end{gathered}`

ANSWER:

`\begin{gathered} Question\text{ A: }(1)/(2) \\ \\ \text{Question B: }\frac{\sqrt[]{2}}{2} \end{gathered}`