Question

Solve the equation for values of x between 0° and 360° inclusive :


6sinxcosx - 6cosx - 5sinx + 5 = 0​

Answer 1

Answer:

Find all values of x between 0 and 360 degrees that satisfy the equation 6cos(x)^2+5sin(x)=2. Give your answer to the nearest tenth of a degree.

..

6cos^2x+5sinx=2

6(1-sin^2x)+5sinx-2=0

6-6sin^2x+5sinx-2=0

-6sin^2x+5sinx+4=0

6sin^2x-5sinx-4=0

solve by factoring this quadratic equation

(3sinx-4)(2sinx+1)=0

3sinx-4=0

3sinx=4

sinx=4/3 (reject,sinx<=1)

..

2sinx+1=0

sinx=-1/2 (sin is negative in 3rd and 4th quadrants)

ans:

x=7pi/6 and 11pi/6

or 210 deg. and 330 deg.