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

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- Apr 25th 2006, 06:35 PMcheesepieNeed help here
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 - Apr 25th 2006, 08:26 PMCaptainBlackQuote:

Originally Posted by**cheesepie**

$\displaystyle

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

$

RonL - Apr 25th 2006, 08:27 PMearbothQuote:

Originally Posted by**cheesepie**

to 1) There isn't any real solution because in your problem cos(x) = 3/2.

But: $\displaystyle -1 \leq \cos(x) \leq 1$

to 2) A product of two factors is zero if one (or both) factor is zero:

$\displaystyle \sin(x) \cdot \cos(x)=0 \Longleftrightarrow \sin(x)=0\ \vee \ \cos(x)=0$

So $\displaystyle x \in \{0^\circ, 180^\circ,360^\circ, 90^\circ, 270^\circ \}$

to 3)Add cos(x) to both sides of your equation and divide then by cos(x). You'll get the equation:

$\displaystyle \sin(x) = \cos(x) \Longleftrightarrow \tan(x)=1$.

So $\displaystyle x \in \{45^\circ, 225^\circ \}$

Greetings

EB - Apr 25th 2006, 11:59 PMcheesepie
thanx alot for ur reply .. :D