Trigonometry Questions from Jan 21,2025

Browse the Trigonometry Q&A Archive for Jan 21,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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29. \( \sec ^{2} x-\sec x=2 \) 30. \( \sec x \csc x=2 \csc x \) 31. \( 2 \sin x+\csc x=0 \) Solving a Trigonometric Equation In Exercises \( \begin{array}{ll}\mathbf{2 5 - 3 8} \text {, find all solutions of the equation in the interval } \\ \mathbf{0 , 2} \pi) \text {. } \\ \begin{array}{ll}\text { 25. } \cos ^{3} x=\cos x & \text { 26. } \sec ^{2} x-1=0 \\ \text { 27. } 3 \tan ^{3} x=\tan x & \text { 28. } 2 \sin ^{2} x=2+\cos x\end{array}\end{array} \) Solving a Trigonometric Equation In Exercises 25-38, find all solutions of the equation in the interval \( \mathbf{0 , 2 \pi )} \). \( \begin{array}{ll}\text { 25. } \cos ^{3} x=\cos x & \text { 26. } \sec ^{2} x-1=0\end{array} \) Given the equation \( 5\sin(x) - 12\cos(x) = 0 \), use the auxiliary angle method to find all possible values of x within one period. a. \( 353^{\circ} \) b. \( 2 \pi \mathrm{rad} \) c. \( 8 \pi \) Zadanie \( 20 .(0-1) \) kióraz podanych liczb jest ujemna? Wybierz właściwą odpowiedź spośród podanych. \( \begin{array}{ll}\text { A. } \cos 120^{\circ}+\cos 60^{\circ} & \text { C. } \cos 120^{\circ}-\sin 150^{\circ} \\ \text { B. } \cos 60^{\circ}-\cos 120^{\circ} & \text { D. } \cos 120^{\circ}+\sin 150^{\circ}\end{array} \) A wall is to be supported by a wooden pole. In order for a support pole to keep a wall vertical, the angle of elevation of the pole must be within the range of \( 30-60 \) degrees. If the pole is 8 feet long, determine the distance from the base of the wall to position the pole. Show that: \[ \frac{1}{\sec \theta-1}+\frac{1}{\frac{\sec \theta+1}{\operatorname{cosec}^{2} \theta}}=2 \cos \theta+ \] A construction worker needs to build a ramp for wheelchair access. If the height of the entrance is 3 feet and the ramp must create an angle of \( 30^{\circ} \) with the ground, what is the length of the ramp? e) \( \cot \theta+\tan \theta=2 \csc 2 \theta \)
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