Question

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

angle (without a calculator/ you may use left hand rule or unit circle)

Answer 1

`\cos(150) = -(\sqrt 3)/(2)`

Step-by-step 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) = (\sqrt 3)/(2)`

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`\cos(150) = -(\sqrt 3)/(2)`