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15.07.2022 - 10:40

Find the value of each of the six trigonometric functions of the angle\theta in the figure. (right triangle)

Question:

Find the value of each of the six trigonometric functions of the angle {eq}\theta{/eq} in the figure.

Answers (1)

Wilma April 5, 2023 в 16:01

The given figure is a right triangle with one angle measuring {eq}theta {/eq} and sides of length 12, 16, and 20. Using the definitions of the six trigonometric functions, we can find their values: - sine: sin({eq}theta {/eq}) = opposite/hypotenuse = 12/20 = 3/5 - cosine: cos({eq}theta {/eq}) = adjacent/hypotenuse = 16/20 = 4/5 - tangent: tan({eq}theta {/eq}) = opposite/adjacent = 12/16 = 3/4 - cosecant: csc({eq}theta {/eq}) = hypotenuse/opposite = 20/12 = 5/3 - secant: sec({eq}theta {/eq}) = hypotenuse/adjacent = 20/16 = 5/4 - cotangent: cot({eq}theta {/eq}) = adjacent/opposite = 16/12 = 4/3 Therefore, the values of the six trigonometric functions of the angle {eq}theta {/eq} in the figure are: - sin({eq}theta {/eq}) = 3/5 - cos({eq}theta {/eq}) = 4/5 - tan({eq}theta {/eq}) = 3/4 - csc({eq}theta {/eq}) = 5/3 - sec({eq}theta {/eq}) = 5/4 - cot({eq}theta {/eq}) = 4/3

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