4.4+Trigonometric+Equations+of+Quadratic+Type

Ex.1 Equation solved by factoring Find all solutions [0, 2p) sin2x=sinx 2sinxcosx=sinx 2sinx cosx-sinx=0 sinx(2cosx-1)=0 sinx=0 2cosx-1=0 x= inverse sin(0) 2cosx=1 x= 0+2pk cosx=1/2 x= p+ 2pk x= inverse cos(1/2) x= p/3 + 2kp x=5p/3+2kp solutions {o, p/3, p, 5p/3} Ex. 2 Using the qaudratic formula find all solutions [0, 360) cos^2a-.2sina=.9 1-sin^2a-.2sina=.9 sin^2a+.2a-.1=0 a= 1, b=.2, c=-.1

sina= -.2+or- squareroot (.2)^2- (4)(-.1)/2 sina= .2317, -.4317 a=inversesin (.2317) a= inversesin (-.4317) a= 13.4+360k a= 205.8+360k a= 166.6+360k a= 334.2+360k use quadrants to determine whether sine is negative or positive

Ex.3 Squaring if there's sec or cosecant, cotangent, etc. use squaring get everything either all sine, cosine, etc. then solve like the other examples