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Alenkasestr [34]
3 years ago
12

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

SAT
1 answer:
Molodets [167]3 years ago
4 0

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)

-----------------------------------------------

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

-----------------------------------------------

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

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