12. -2 points SPreCalc7 7.5.029. An equation is given. (Enter your answers as a
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12. -2 points SPreCalc7 7.5.029. An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 2 sin(e)-cos(26) (a) Find all solutions of the equation (b) Find the solutions in the interval [0, 2?). Need Help? ReadItWatch R 13. ? ?1 points SPreCalc7 7.5.031 Solve the equation by factoring. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 3 tan3(8) + 3 tan2(9)-tan(?)-1-0 Need Help? 14.-1 points SProCalc? 7.5.033. Solve the equation by factoring. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 2 sin(8) tan(8) +tan(e)2 sin(e)Explanation / Answer
1) 1 - 2 sin theta = cos 2 theta
1 - 2 sin theta - cos 2 theta = 0
1 - cos 2 theta = 2 sin^2 theta
2 sin^2 theta - 2 sin theta = 0
2 ( sin^2 theta -1 ) = 0
sin theta = 1 , 0
theta = pi/2 + 2kpi , 2kpi , pi + 2kpi
b) solution in the interval [ 0 , 2pi )
theta = 0 , pi , pi/2
13) 3 tan^3 theta + 3 tan^2 theta - tan theta -1 = 0
3 tan^2 theta ( tan theta + 1 ) - 1 ( tan theta + 1 ) = 0
( 3 tan^2 theta -1 ) ( tan theta + 1 ) = 0
tan theta = +- 1 / sqrt 3 , -1
theta = pi/6 + kpi , 3pi/4 + kpi , 5pi/6 + kpi
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