# `-pi/6` Evaluate the sine, cosine and tangent of the angle without using a calculator.

Asked on by nick-teal

### Textbook Question

Chapter 4, 4.4 - Problem 63 - Precalculus (3rd Edition, Ron Larson).
See all solutions for this textbook.

shmindle | Student, Grade 11 | (Level 2) Honors

Posted on

-pi/6 on the unit circle diagram is the same as 11pi/6.  Think about it as going pi/6 counterclockwise, instead of clockwise.

When evaluating sine, think about the y axis.  The -pi/6 on the unit circle would horizontally match up with -1/2 on the y axis if you drew a line starting from the intersection of the edge of the circle  and -pi/6 that was parallel to the x axis.  Thus, sine of -pi/6 is -1/2.

When evaluating cosine, think of the same as sine but with the x axis.  The cosine of -pi/6 is √3/2 .

When evaluating tangent, it is useful to look at the numbers outside the parentheses in the chart I attached below.  The tangent of -pi/6 is -√3/3.

You can use a calculator to verify.

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

We’ve answered 319,644 questions. We can answer yours, too.