Expert: Sherman D. - 11/3/2004

Question
Find to the nearest tenth of a degree all nonegative values of theta less than 30 degrees
sin(theta)+3cos(2 theta)=1.

Answer
sin(theta) + 3cos(2 theta) = 1

i prefer to type it like this

sinA + 3cos(2A) = 1

sinA + 3(cosAcosA - sinA sinA) = 1

sinA + 3((cosA)^2 - (sinA)^2) = 1

sinA + 3(1 - 2(sinA)^2) = 1

sinA + 3 - 6(sinA)^2 = 1

sinA - 6(sinA)^2 + 2 = 0

I got about there and i quit trying to explain exactly how to get it. I tried figuring it out using the quadratic formula and by replacing sinA with "x". Anyway, i went to www.quickmath.com, clicked on Solve under Equations, then i typed in sin(x) + 3cos(2x) = 1, and it gave me 4 values, but since i couldn't figure out how to get the last 2, i just typed down the first 2 it gave me.

theta = -150 or -30