F.TF.B.6: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

Example Problems

Suppose that

\cos \theta = \frac{2}{5}

and that

\theta

is in the 4th quadrant. Find

\sin \theta

and

\tan \theta

exactly.

The following are all angle measures (in radians, rounded to the nearest hundredth) whose sine is

0.34

.
Which is the principal value of

\arcsin(0.34)

?

The following are all angle measures (in radians, rounded to the nearest hundredth) whose sine is

-0.66

.
Which is the principal value of

\arcsin(-0.66)

?

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