trigonometry

Asked by ashwinivg | 25th Jun, 2010, 02:46: PM

Expert Answer:

Dear student, following is the answer to your query:
6 cos θ + 8 sin θ = A sin(θ + α)
 
Using the result, sin(x+y) = sinx cosy + cosx siny, in RHS, 
6 cos θ + 8 sin θ = A sin θ cos α + A sin α  cos θ
 
Now comparing both sides we find,
 
6 = A sin α  and 8 = A cos α
 
or sin α = 6/A and cos α = 8/A
 
Now squaring these results and adding them, we get:
 
sin2α +  cos2α = 36/A2 + 64/A2
 
36/A2 + 64/A2 = 1
 
A2 = 100
 
A = ±10
Regards
TopperLearning

Answered by  | 14th Jul, 2010, 02:16: PM

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