# Math Help - Solving Trigonometric Equations

1. ## Solving Trigonometric Equations

Solve this trigonometric equation $0^o {\leq} x {\leq} 360^o$

$cos^2x+7sinxcosx=3$

Find the value of $x$ (in degrees).

2. Originally Posted by acevipa
Solve this trigonometric equation $0^o {\leq} x {\leq} 360^o$

$cos^2x+7sinxcosx=3$

Find the value of $x$ (in degrees).
$\Rightarrow 2 \cos^2 x + 14 \sin x \cos x = 6$

$\Rightarrow (\cos (2x) + 1) + 7 \sin (2x) = 6$

$\Rightarrow \cos (2x) + 7 \sin (2x) = 5$.

There is a standard technique for converting the left hand side into the form $A \sin (2x + \phi)$. Can you do that (read http://www.mathcentre.ac.uk/resource...a-alphaetc.pdf ). Then the equation becomes

$\sin (2x + \phi) = \frac{5}{A}$

which is easy.