Sine & Cosine Problems

  • Thread starter Caldus
  • Start date
106
0
I'm unsure as to whether I'm correct with this:

4sinx - 3cosx

My answer ended up being 5sin(x + sin^-1 (-3/5)).

The equations I used were:

asinx + bcosx = (a^2 + b^2)^1/2 * sin(x + angle)
angle = sin^-1 (b / (a^2 + b^2)^1/2))

Can someone clarify whether I'm correct? I would appreciate it.
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
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17
A good way to check your answer is to reverse the process using the angle addition identity:

sin (θ + φ) = sin θ cos φ + cos θ sin φ

And using the facts

sin arcsin (3/5) = 3/5
and
cos arcsin (3/5) = 4/5. (why?)
 
106
0
I checked my answer and it equals the original equation, but have I fully solved it?
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,845
17
If it checks (and I agree that it does), then yep!
 

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