# 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

1. 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

posted by drwls
2. drwls,
that is amazingly clever.

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

posted by usha
4. 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.

posted by drwls

First Name

## Similar Questions

1. ### 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 ...
2. ### trignometry

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
3. ### 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.
4. ### 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
5. ### 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. |
6. ### trig

cosθ =5/13 with -π/2 < θ <0 find each of the following sin( θ - 5π/4) cos( θ - 11π/6) tan( θ + 5π/4) can some1 explain to me how to do these? im completely lost and this is the
7. ### trig

The terminal side of θ lies on a given line in the specified quadrant. Find the values of the six trigonometric functions of θ by finding a point on the line. Line: (55/48)x Quadrant:III sin(θ)= cos(θ)=
8. ### 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
9. ### 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?
10. ### maths

if alpha and beta are the zeros of the polynomial 2x^2-4x+5 then find the values of (i)alpha^2+beta^2 (ii)1/alpha^2+1/beta^2 (iii)(r)alpha/beta+(r)beta/alpha (iv)alpha^-1+beta^-1

More Similar Questions