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Exercises Trigonometry

Example 8 from Algebra and Trigonometry, 9.5 Solving Trigonometric Equations

Using a Calculator to Solve a Trigonometric Equation Involving Sine

Use a calculator to solve the equation $\sin θ = 0.8,$ where $θ$ is in radians.

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
Make sure mode is set to radians. To find $θ,$ use the inverse sine function. On most calculators, you will need to push the 2^ND button and then the SIN button to bring up the $\sin^{- 1}$ function. What is shown on the screen is $\sin^{- 1} (.$ The calculator is ready for the input within the parentheses. For this problem, we enter $\sin^{- 1} (0.8),$ and press ENTER. Thus, to four decimals places,
$\sin^{- 1} (0.8) \approx 0.9273$

The solution is

$θ \approx 0.9273 \pm 2 π k$

The angle measurement in degrees is

$\begin{matrix} θ & \approx & 53.1° \\ θ & \approx & 180° - 53.1° \\ \approx & 126.9° \end{matrix}$

How did it go?

PreviousIdentify all Solutions to the Equation Involving Tangent Next Using a Calculator to Solve a Trigonometric Equation Involving Secant

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 9.5, 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.