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Evaluating Trigonometric Functions of Angles Not in Standard Position · Physics Playground

Exercises Trigonometry

Example 2 from Algebra and Trigonometry, 7.2 Right Triangle Trigonometry

Evaluating Trigonometric Functions of Angles Not in Standard Position

Using the triangle shown in Figure 6, evaluate $\sin α, \cos α, \tan α, sec α, \csc α, and \cot α .$

Right triangle with sides of 3, 4, and 5. Angle alpha is also labeled which is opposite the side labeled 4.

Figure 6

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
$\begin{matrix} sin α & = \frac{opposite α}{hypotenuse} & = \frac{4}{5} \\ cos α & = \frac{adjacent to α}{hypotenuse} & = \frac{3}{5} \\ tan α & = \frac{opposite α}{adjacent to α} & = \frac{4}{3} \\ sec α & = \frac{hypotenuse}{adjacent to α} & = \frac{5}{3} \\ csc α & = \frac{hypotenuse}{opposite α} & = \frac{5}{4} \\ cot α & = \frac{adjacent to α}{opposite α} & = \frac{3}{4} \end{matrix}$

Your turn

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

Using the triangle shown in Figure 7,evaluate $sin t, cos t, tan t, sec t, csc t, and cot t .$

Right triangle with sides 33, 56, and 65. Angle t is also labeled which is opposite to the side labeled 33.

Figure 7

How did it go?

PreviousEvaluating a Trigonometric Function of a Right Triangle Next Evaluating Trigonometric Functions of Special Angles Using Side Lengths

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 7.2, 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.

Solution

Your turn