Friday

August 1, 2014

August 1, 2014

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

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 6:57amtheta = 209,55192°

theta = 76,70829°

- 12th grade Trigonometry -
**MathMate**, Friday, March 4, 2011 at 12:48pmSum 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°

**Related Questions**

Trigonometry - Solve the following trig equations. Give all positive values of ...

Trigonometry - I have some trigonometric equations to do, but I'm pretty lost, ...

trigonometry (please double check this) - Solve the following trig equations. ...

trigonometry (please double check this) - Solve the following trig equations. ...

math - Can anyone help w/ these. 1) Solve the equation in the internal [0deg, ...

Trigonometry - Let S be the sum of all the possible values of sin x that satisfy...

math - find to the nearest minute, all positive values in the interval 0° ≤...

math - find to the nearest minute, all positive values in the interval 0° ≤...

Trigonometry - I really need help with this trigonometry question.please any ...

algebra - What are the intercepting points of y^2=-4x and x^2=y I set both ...