Posted by usha on Saturday, June 11, 2011 at 6:54am.
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
trig - drwls, Saturday, June 11, 2011 at 7:55am
0.6 cosè + 0.8 sinè = 0.9
Let sinx = 0.6; then
cosx = 0.8 and x = 36.87 degrees
sinx cosè + cosx sinè = 0.9
sin (x + è) = 0.9
x + è = 64.16 degrees or 115.84 degrees
alpha = è1 = 27.29 degrees
beta = è2 = 78.97
alpha + beta = 106.26 degrees
sin (alpha + beta) = 0.9600
trig - Reiny, Saturday, June 11, 2011 at 8:16am
that is amazingly clever.
trig - usha, Saturday, June 11, 2011 at 10:21am
thank you very much. can u solve the same by quadratic equation method
trig - drwls, Saturday, June 11, 2011 at 11:24am
yes, it can be done that way, but I'd rather leave that to you.
Write it as
6cosθ= 9 - 8 sinθ
Square both sides and the left side can be written 36(1 - sin^2 θ)
Then you have a quadratic in sin theta to solve. Have fun.
Answer This Question
More Related Questions
- math - if alpha and beta are 2 different values of θ lying between 0 and 2...
- trignometry - if alpha and beta are 2 different values of θ lying between 0...
- 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 ...
- Math - Calculus - The identity below is significant because it relates 3 ...
- trig - cosθ =5/13 with -π/2 < θ <0 find each of the ...
- Trig - Given that csc θ = -4 and tan θ > 0, find the exact value of...
- trig - If sin alpha = -3/5, sin beta = -5/13, P(alpha) is in the third quadrant...
- mathematics - given sinθ=-5/13 and π<θ<3π/2 find sin2...
- math - given sinθ=-5/13 and π<θ<3π/2 find sin2θ ...