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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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