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Exercises Trigonometry

Example 2 from Algebra and Trigonometry, 9.5 Solving Trigonometric Equations

Solving a Linear Equation Involving the Sine Function

Find all possible exact solutions for the equation $\sin t = \frac{1}{2} .$

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
Solving for all possible values of t means that solutions include angles beyond the period of $2 π .$ From Figure 2, we can see that the solutions are $t = \frac{π}{6}$ and $t = \frac{5 π}{6} .$ But the problem is asking for all possible values that solve the equation. Therefore, the answer is
$t = \frac{π}{6} \pm 2 π k and t = \frac{5 π}{6} \pm 2 π k$
where $k$ is an integer.

How did it go?

PreviousSolving a Linear Trigonometric Equation Involving the Cosine Function Next Solve the Linear Trigonometric Equation

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.