trignometry
posted by usha .
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
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(1x^2) + 8 x = 9
6 sqrt (1x^2) = 98x
36 (1x^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
Respond to this Question
Similar Questions

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 … 
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 
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 ... 
math
given sinθ=5/13 and π<θ<3π/2 find sin2θ cos( θ4π/3) sin(θ/2) can some1 explain to me how to do these? 
math
if cosθ=2/3 and tanθ<0 find the exact value sin(θ5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me? 
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( θ4π/3) sin(θ/2) can some1 explain this to me … 
trigonometry
if cosθ=2/3 and tanθ<0 find the exact value sin(θ5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me? 
mathematics
given sinθ=5/13 and π<θ<3π/2 find sin2θ cos( θ4π/3) sin(θ/2) can some1 please help me with this? 
trig
evaluate the following in exact form, where the angeles alpha and beta satisfy the conditions: sin alpha=4/5 for pi/2 < alpha < pi tan beta=7/24 for pie < beta < 3pi/2 answer choices A. sin(beta+alpha) B. tan(betaalpha) … 
Precalc/Trig
Sorry there are quite a few problems, but I just need to know if these are correct (and if they aren't, where I went wrong): 1. Solve these equations. tanθ = √3 θ = 2π/3 + kπ θ = 5π/3 + kπ …