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Home Question Bank Math Trigonometry Archive 2024 December 12

Trigonometry Questions from Dec 12,2024

Browse the Trigonometry Q&A Archive for Dec 12,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Find the amplitude, period, and phase shift of the function. Graph the function. Be sure to label key points. Show at least two periods. \( y=6 \) cos \( \left(2 x-\frac{\pi}{2}\right) \) What is the amplitude? (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression.) What is the period? \( \square \) (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression.) What is the phase shift? \( \square \) Tom wants to clean his second story windows and plans to buy a ladder that will reach at least 20 feet high. If he leans the ladder against the house so that the base of the ladder makes a 59 degree angle with the ground, how long of a ladder should he buy? Round to a whole number as necessary. The ladder length is \( \square \) feet. (Round to a whole number as needed.) Identify the transformations for the function \( f(x)=3 \cos \left(-x+\frac{\pi}{3}\right)-2 \). ( 1 point) vertical stretch by a factor of 3 , reflection over the \( y \)-axis, horizontal shift right by \( \frac{\pi}{3} \), and vertical shift down 2 vertical stretch by a factor of 3 , reflection over the \( y \)-axis, horizontal shift right by \( \frac{\pi}{3} \), and vertical shift up 2 vertical stretch by a factor of 3 , horizontal compression by -1 , horizontal shift night by \( \frac{\pi}{3} \), and . vertical shift down 2 vertical stretch by a factor of 3 , reflection over the \( y \)-axis, horizontal shift left by \( \frac{\pi}{3} \), and vertical shift down 2 \( 179 ^ { \circ } 59 ^ { \prime } 60 ^ { \prime \prime } - 103 ^ { \circ } 31 ^ { \prime } 14 ^ { \prime \prime } \) The graph of \( f(x)=\sin (x+c) \) is shifted \( \frac{\pi}{3} \) units left when compared to the graph of \( g(x)=\sin (x) \). What is the value of \( c \) ? (1 point) \( c=\square \) \( 179 ^ { \circ } 59 ^ { \prime } 60 ^ { \prime \prime } - 103 ^ { \circ } 31 ^ { \prime } 14 ^ { \prime \prime } \) Which of the following correctly describes the phase shift of the function \( f(x)=2 \sin \left(x+\frac{\pi}{6}\right) \) ? (1 point) \( 0 . \frac{\pi}{6} \) \( \frac{\pi}{2} \) If \( \tan \left(3 \theta-70^{\circ}\right) \times \tan \theta=1 \) where \( \left.\theta \in\right] 0, \frac{\pi}{3}[ \), then \( \sin (2 \theta+10)= \) Find the period and write the equation of the sine function that has a maximum at \( \left(\frac{\pi}{14}, 1\right) \) and a minimum at \( \left(\frac{3 \pi}{14},-1\right) \). (1 point) period \( =\square \) \( f(x)=\sin (\square) \) Determine the equation for a sinefunction that has a horizontal compression by a factor of 3 and a reflection across the \( x \)-axis. (1 point) \( \begin{array}{l}f(x)=\sin (-3 x) \\ f(x)=\sin \left(-\frac{1}{3} x\right) \\ f(x)=-3 \sin x \\ f(x)=\sin \left(\frac{1}{3} x\right)\end{array} \)
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