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[latex]250°[/latex]
Chapter 5: Equations and Identities
Practice each skill in the Homework Problems listed:
For Problems 1–4, find the reference angle. (If you would like to review reference angles, see Section 4.1.)
[latex]250°[/latex]
[latex]145°[/latex]
[latex]320°[/latex]
[latex]-110°[/latex]
For Problems 5–8, find an angle in each quadrant with the given reference angle.
[latex]18°[/latex]
[latex]35°[/latex]
[latex]52°[/latex]
[latex]78°[/latex]
For Problems 9–14,
For Problems 15–18, use a graph to solve the equation. Check your solution by substitution.
[latex]\dfrac{-1}{3}x^2 + \dfrac{2}{3}x + 5 = 0[/latex]
[latex]0.0625x^2 + 0.5 x = -1[/latex]
[latex]x^3 + 2x^2 - 6 = 2x^2 + 7x[/latex]
[latex]8 - 12x + 6x^2 - x^3[/latex]
For Problems 19–32, solve the equation exactly for [latex]0° \le\theta\lt 360°{.}[/latex]
[latex]3\tan \theta = \\\sqrt{3}[/latex]
[latex]7\sin \theta + 11 = 11[/latex]
[latex]3 = 5 - 4\cos \theta[/latex]
[latex]6\tan \theta + 21 = 15[/latex]
[latex]8\sin \theta + 5 = 1[/latex]
[latex]9\cos \theta + 15 = 6[/latex]
[latex]0 = \\\sqrt{2} + 2\sin \theta[/latex]
[latex]\\\sqrt{3}\cos \theta = -\dfrac{3}{2}[/latex]
[latex]\cos^2 \theta - 1 = 0[/latex]
[latex]1 - \sin^2 \theta = 0[/latex]
[latex]4\sin^2 \theta - 3 = 0[/latex]
[latex]0 = 1 - 2\cos^2 \theta[/latex]
[latex]1 - \tan^2 \theta = 0[/latex]
[latex]0 = 6 \tan^2 \theta - 2[/latex]
For Problems 33–38, solve the equation for [latex]0° \le\theta\lt 360°{.}[/latex] Round your answers to two decimal places.
[latex]\dfrac{1}{2}\tan \theta - 1 = -3[/latex]
[latex]3\tan \theta - 2 = 4[/latex]
[latex]3 = 5\cos \theta[/latex]
[latex]4 = 6\sin \theta[/latex]
[latex]7 \sin \theta + 2 = 1[/latex]
[latex]2 = 5 - \dfrac{1}{3} \tan \theta[/latex]
For Problems 39–46, use a graph to estimate the solutions for angles between [latex]0°[/latex] and [latex]360°{.}[/latex] Solve the equation algebraically.
[latex]7 - \tan A = 8[/latex]
[latex]6 = 8\tan w - 2[/latex]
[latex]5 = 1 - 8\sin \phi[/latex]
[latex]9 - 4\sin t = 13[/latex]
[latex]2\cos B - 2 = -2[/latex]
[latex]2 - 6\cos u = 5[/latex]
[latex]3 = 2\sin \theta + 4[/latex]
[latex]5 = 3\cos x + 5[/latex]
For Problems 47–52, use a graph to estimate the solutions for angles between [latex]0°[/latex] and [latex]360°{.}[/latex] Solve the equation algebraically, rounding angles to the nearest degree.
[latex]8\sin t + 7 = 4[/latex]
[latex]9 - 6\cos A = 5[/latex]
[latex]5\tan B - 4 = -2[/latex]
[latex]3 - 10\tan C = -11[/latex]
[latex]1 + 6\cos \phi = -4[/latex]
[latex]4\sin u - 2 = -1[/latex]
For Problems 53–64, solve the equation for [latex]0° \le\theta\le 360°{.}[/latex] Round angles to two decimal places.
[latex]6\cos^2 \theta = 2[/latex]
[latex]2 - 7\sin^2 \phi = 1[/latex]
[latex]5\sin^2 \theta + \sin \theta = 0[/latex]
[latex]4\tan^2 \theta = \tan \theta[/latex]
[latex]2\cos^2 \theta + \cos \theta - 1 = 0[/latex]
[latex]\tan^2 \theta - 5\tan \theta + 6 = 0[/latex]
[latex]6\tan^2 \theta - \tan \theta - 1 = 0[/latex]
[latex]10\cos^2 \theta