Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

12. -2 points SPreCalc7 7.5.029. An equation is given. (Enter your answers as a

ID: 2912383 • Letter: 1

Question

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