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**cheesepie** · April 25th 2006, 06:35 PM

Trigonometric formulas,identites and equation

solve each equation for nonnegative angles less than 360deg or 2 pi

1)2cos x=3
2)sinxcosx=0
3)sin theta - cos theta=0

**CaptainBlack** · April 25th 2006, 08:26 PM

Originally Posted by cheesepie

1)2cos x=3

Not possible if we are restricted to real angles as:

$<br /> 2 \cos(x)=3$ means that $\cos(x)=3/2 >1 <br />$

RonL

**earboth** · April 25th 2006, 08:27 PM

Originally Posted by cheesepie

Trigonometric formulas,identites and equation

solve each equation for nonnegative angles less than 360deg or 2 pi

1)2cos x=3
2)sinxcosx=0
3)sin theta - cos theta=0

Hello,

to 1) There isn't any real solution because in your problem cos(x) = 3/2.
But: $-1 \leq \cos(x) \leq 1$

to 2) A product of two factors is zero if one (or both) factor is zero:
$\sin(x) \cdot \cos(x)=0 \Longleftrightarrow \sin(x)=0\ \vee \ \cos(x)=0$
So $x \in \{0^\circ, 180^\circ,360^\circ, 90^\circ, 270^\circ \}$

to 3)Add cos(x) to both sides of your equation and divide then by cos(x). You'll get the equation:
$\sin(x) = \cos(x) \Longleftrightarrow \tan(x)=1$ .
So $x \in \{45^\circ, 225^\circ \}$

Greetings

EB

**cheesepie** · April 25th 2006, 11:59 PM

thanx alot for ur reply ..

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