## Trigonometric Function Analysis and Problem Solving### Problem 1: Graphing the Function**Task:**Graph one cycle of the trigonometric function \( f(x) = 2\cos(x - \pi) + 1 \).### Problem 2: Function Characteristics**Task:**Find the period, amplitude, phase shift, and vertical shift of the function in Problem 1.### Problem 3: Solving Trigonometric Equations**Task:**Solve the equation, giving the exact solutions which lie in the interval \([0, 2\pi)\):\[ \cos(2x) = 5\sin(x) - 2 \]### Problem 4: Solving Trigonometric Equations**Task:**Solve the equation, giving the exact solutions which lie in the interval \([0, 2\pi)\):\[ 2\tan(x) = 1 - \tan^2(x) \]### Problem 5: Solving for Sides and Angles**Task:**Solve for the remaining side(s) and angle(s), if possible. The pairs \((\alpha, a)\), \((\beta, b)\), and \((\gamma, c)\) are angle-side opposite pairs.Given:\[ \alpha = 22^\circ, \quad \beta = 33^\circ, \quad a = 4 \]### Diagrams and Graphs:- **Function Graph:** (No diagram provided in the text, manual graphing or use of graphing software recommended.)- **Equations and Solutions:** - Visualization of solutions on the unit circle might be helpful for Problems 3 and 4. - Triangle diagrams showing angles and sides for Problem 5 may assist in solving using the Law of Sines or the Law of Cosines.Understanding and visualizing these trigonometric concepts will aid in effectively solving and graphing the given problems.

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Graph one cycle of the trig function f(x) = 2cos(x – T) + 1 Find the period, amplitude, phase shift and vertical shift of the function in #1. Solve the equation, giving the exact solutions which lie in [0, 2n) cos(2x) = 5sin(x) – 2 Solve the equation, giving the exact solutions which lie in [0, 2n) 2tan(x) = 1 – tan²(x) Solve for the remaining side(s) and angle(s), if possible. (a, a), (B, b), and (y, c) are angle-side opposite pairs. a = 22°, B = 33°, a = 4

Graph one cycle of the trig function f(x) = 2cos(x – T) + 1 Find the period, amplitude, phase shift and vertical shift of the function in #1. Solve the equation, giving the exact solutions which lie in [0, 2n) cos(2x) = 5sin(x) – 2 Solve the equation, giving the exact solutions which lie in [0, 2n) 2tan(x) = 1 – tan²(x) Solve for the remaining side(s) and angle(s), if possible. (a, a), (B, b), and (y, c) are angle-side opposite pairs. a = 22°, B = 33°, a = 4

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 64E

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