# trig

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

1. drwls

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

2. Reiny

drwls,
that is amazingly clever.

3. usha

thank you very much. can u solve the same by quadratic equation method

4. drwls

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.

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