Question

Show an example of how to evaluate a trigonometric function using reference

Answer 1

Answer:

$\cos(150) = -\frac{\sqrt 3}{2}$

Explanation:

An example is as follows;

Using reference angle, evaluate $\cos(150)$

Solution:

We have: $\cos(150)$

150 degrees is in the second quadrant, and it makes 30 degrees (i.e. 180 - 150) with the x-axis.

This implies that, cos(150) has the same magnitude as cos(30);

The only difference in the values is the sign; because

• 30 degrees is in the first quadrant where all functions are positive

• 150 degrees is in the third quadrant where all cosine is negative

So, we have:

$\cos(150) = -\cos(30)$

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$\cos(30) = \frac{\sqrt 3}{2}$

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$\cos(150) = -\frac{\sqrt 3}{2}$