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1. Draw a right triangle. Label the longer leg "1", the shorter leg "x", and the angle between the longer leg and the hypotenuse. Assume 0 is measured in radians. a.) Find tan(0). b.) Find tan-¹(x). c.) Find the hypotenuse of the triangle as a function of x. d.) Find sin(tan'(x)) as a ratio involving no trig functions. e.) Find sec(tan-¹(x)) as a ratio involving no trig functions. f.) If x<0, then tan(x) is a negative angle in quadrant g.) Explain why your answers to parts d.) and e.) are still valid for x<0.

1. Draw a right triangle. Label the longer leg "1", the shorter leg "x", and the angle between the longer leg and the hypotenuse. Assume 0 is measured in radians. a.) Find tan(0). b.) Find tan-¹(x). c.) Find the hypotenuse of the triangle as a function of x. d.) Find sin(tan'(x)) as a ratio involving no trig functions. e.) Find sec(tan-¹(x)) as a ratio involving no trig functions. f.) If x<0, then tan(x) is a negative angle in quadrant g.) Explain why your answers to parts d.) and e.) are still valid for x<0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 59E
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1. Draw a right triangle. Label the longer leg "1", the shorter leg "x", and the angle between the longer leg and the hypotenuse. Assume 0 is measured in radians. a.) Find tan(0). b.) Find tan-¹(x). c.) Find the hypotenuse of the triangle as a function of x. d.) Find sin(tan'(x)) as a ratio involving no trig functions. e.) Find sec(tan-¹(x)) as a ratio involving no trig functions. f.) If x<0, then tan(x) is a negative angle in quadrant g.) Explain why your answers to parts d.) and e.) are still valid for x<0.
Transcribed Image Text:1. Draw a right triangle. Label the longer leg "1", the shorter leg "x", and the angle between the longer leg and the hypotenuse. Assume 0 is measured in radians. a.) Find tan(0). b.) Find tan-¹(x). c.) Find the hypotenuse of the triangle as a function of x. d.) Find sin(tan'(x)) as a ratio involving no trig functions. e.) Find sec(tan-¹(x)) as a ratio involving no trig functions. f.) If x<0, then tan(x) is a negative angle in quadrant g.) Explain why your answers to parts d.) and e.) are still valid for x<0.
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