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Exercises Trigonometry

Example 1 from Algebra and Trigonometry, 8.3 Inverse Trigonometric Functions

Writing a Relation for an Inverse Function

Given $\sin (\frac{5 π}{12}) \approx 0.96593,$ write a relation involving the inverse sine.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Use the relation for the inverse sine. If $\sin y = x,$ then $\sin^{- 1} x = y$ .

In this problem, $x = 0.96593,$ and $y = \frac{5 π}{12} .$

$\sin^{- 1} (0.96593) \approx \frac{5 π}{12}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Given $\cos (0.5) \approx 0.8776,$ write a relation involving the inverse cosine.

How did it go?

PreviousUsing Trigonometric Functions to Solve Real-World Scenarios Next Evaluating Inverse Trigonometric Functions for Special Input Values

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 8.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.