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Exercises Trigonometry

Example 3 from Algebra and Trigonometry, 9.5 Solving Trigonometric Equations

Solve the Linear Trigonometric Equation

Solve the equation exactly: $2 \cos θ - 3 = - 5, 0 \leq θ < 2 π .$

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 algebraic techniques to solve the equation.

$\begin{matrix} 2 \cos θ - 3 & = & - 5 \\ 2 \cos θ & = & - 2 \\ \cos θ & = & - 1 \\ θ & = & π \end{matrix}$

Your turn

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

Solve exactly the following linear equation on the interval $[0, 2 π) : 2 \sin x + 1 = 0.$

How did it go?

PreviousSolving a Linear Equation Involving the Sine Function Next Solving a Problem Involving a Single Trigonometric Function

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.