# Trigonometric Equations

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

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 Î± is equal to:

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

Solving further, we have:

Therefore, we have:

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