Posted by **usha** on Saturday, June 11, 2011 at 11:14am.

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 -
**Damon**, Saturday, June 11, 2011 at 1:34pm
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

## Answer this Question

## Related Questions

- math - if alpha and beta are 2 different values of θ lying between 0 and 2...
- trig - if alpha and beta are 2 different values of θ lying between 0 and 2...
- Math - Calculus - The identity below is significant because it relates 3 ...
- trig - evaluate the following in exact form, where the angeles alpha and beta ...
- Precalc/Trig - Sorry there are quite a few problems, but I just need to know if ...
- Calculus - A vehicle moves along a straight path with a speed of 4m/s. A ...
- mathematics - given sinθ=-5/13 and π<θ<3π/2 find sin2...
- math - given sinθ=-5/13 and π<θ<3π/2 find sin2θ ...
- trigonometry - if cosθ=2/3 and tanθ<0 find the exact value sin(&#...
- math - if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5&#...

More Related Questions