trignometry

posted by .

if alpha and beta are 2 different values of θ lying between 0 and 2π which satisfy the equation 6cosθ+8 sinθ=9 find the value of sin alpha + beta.i want the answer by quadratic method. can u help solving sum by that method

• trignometry -

Oh well, if you do not like WLS' cool method then

cos T = sqrt(1 - sin^2 T)

6 sqrt(1 -sin^2 T) + 8 sin T = 9
let sin T = x

6 sqrt(1-x^2) + 8 x = 9

6 sqrt (1-x^2) = 9-8x

36 (1-x^2) = 81 - 144x + 64 x^2
36 -36 x^2 = 81 - 144x + 64 x^2
100 x^2 -144 x + 45 = 0
x = [ 144 +/- sqrt (20736 - 18000)]/200
x = [ 144 +/- 52.3 ]/200
x = .981 or .4585
but x is sin T so
T = 78.8 or T = 27.3
sum = 106.1
sin(106.1) = .961

Similar Questions

1. Math - Calculus

The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below. | a …
2. trig

if alpha and beta are 2 different values of θ lying between 0 and 2π which satisfy the equation 6cosθ+8 sinθ=9 find the value of sin alpha + beta
3. math

if alpha and beta are 2 different values of θ lying between 0 and 2π which satisfy the equation 6cosθ+8 sinθ=9 find the value of sin alpha + beta ...
4. math

given sinθ=-5/13 and π<θ<3π/2 find sin2θ cos( θ-4π/3) sin(θ/2) can some1 explain to me how to do these?
5. math

if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me?
6. trigonometry

given tanθ= -2√10/3 and π/2<θ< π find: sin2θ tan θ/2 given sinθ=-5/13 and π<θ<3π/2 find sin2θ cos( θ-4π/3) sin(θ/2) can some1 explain this to me …
7. trigonometry

if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me?