Posted by **anon** on Friday, March 4, 2011 at 6:31am.

Solve this trigonometric equation.give all positive values of the angle between 0deg and 360deg that will satisfy.

Give any approximate value to the nearest minute only.

3 sin theta - 4 cos theta = 2

- 12th grade Trigonometry -
**shin**, Friday, March 4, 2011 at 6:57am
theta = 209,55192°

theta = 76,70829°

- 12th grade Trigonometry -
**MathMate**, Friday, March 4, 2011 at 12:48pm
Sum or difference of sin(θ) and cos(θ) can be solved in the following way, if you are familiar with the sum and difference formulae for sin(a±b).

Given

3sin(θ)-4cos(θ)=2

for a particular φ and amplitude A, we rewrite the above equation as:

Asin(θ-φ)=2

where A=sqrt(3²+4²)=5

or

sin(θ-&phi)=2/5....(1)

=> θ-&phi=asin(2/5)=23.5782°

or 180-23.5782=156.4218°. ...(2)

Expand (1) to get:

sin(θ)cos(&phi)-cos(θ)sin(&phi)=2/5

=> cos(φ)=3/5, sin(φ)=4/5

=> φ=53.1301° or 306.8699°...(3)

So solve for θ from (2) and (3) gives

θ=23.5782+53.1301=76.7083° or θ=156.4218+53.1301=209.5519°

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