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# Trigonometric Equations

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Given that x = 3sin theta and y = 4cos theta,express x + y in the form
R sin (theta + alpha) giving alpha in radians correct to 4 decimal places
and hence solve the equation, 3sin theta + 4cos theta =1.2
giving your answers in radians in the range -Pi to +Pi

© BrainMass Inc. brainmass.com September 29, 2022, 1:26 pm ad1c9bdddf
https://brainmass.com/math/trigonometry/trigonometric-equations-expressions-249807

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Solution:
We will add first X and Y, giving:

We divide and multiply the Right Hand Side by the hypotenuse , we have:

We will have trigonometric values for alpha, with X as the horizontal (cosine) and Y as the vertical (sine):

Therefore, we will have:

Using trigonometric identity to simplify, we have:

Which now has the format of:

Where α is equal to:

Since we have obtained , we will substitute it to , giving us:

Solving further, we have:

Therefore, we have:

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com September 29, 2022, 1:26 pm ad1c9bdddf>
https://brainmass.com/math/trigonometry/trigonometric-equations-expressions-249807