# Thread: Solving trig equations

1. ## Solving trig equations

Hi
I need help on solving some of the following equations:
1) Solve $\displaystyle cos^2(x)-cos(x)sin(x)$ for x = $\displaystyle [0,2\pi]$.

2)Solve sec(x)=2.5 in the interval $\displaystyle [-\pi,\pi]$, giving the answers correct to two decimal places.

P.S

2. Originally Posted by Paymemoney
Hi
I need help on solving some of the following equations:
1) Solve $\displaystyle cos^2(x)-cos(x)sin(x)$ for x = $\displaystyle [0,2\pi]$.

2)Solve sec(x)=2.5 in the interval $\displaystyle [-\pi,\pi]$, giving the answers correct to two decimal places.

P.S
1. What is this expression equal to? If it's equal to 0 then factor

$\displaystyle cos(x)(cos(x)-sin(x)) = 0$

$\displaystyle cos(x)=0$ or $\displaystyle cos(x) = sin(x)$

2.Take the reciprocal of both sides

$\displaystyle cos(x) = \frac{2}{5}$

3. yeh the first question is equal to 0

4. in question 2 I'm not sure if i have done it correct:
$\displaystyle sec(x)=\frac{1}{cos(x)}$
so $\displaystyle \frac{1}{\frac{2}{5}}=2.5*\frac{2}{5}$

5. Originally Posted by e^(i*pi)
1. What is this expression equal to? If it's equal to 0 then factor

$\displaystyle cos(x)(cos(x)-sin(x)) = 0$

$\displaystyle cos(x)=0$ or $\displaystyle cos(x) = sin(x)$
i get two solutions for when cos(x)=0, which are $\displaystyle \frac{\pi}{2}$ & $\displaystyle \frac{3\pi}{2}$.
However how do you get the solutions for cos(x)=sin(x)

6. Originally Posted by Paymemoney
i get two solutions for when cos(x)=0, which are $\displaystyle \frac{\pi}{2}$ & $\displaystyle \frac{3\pi}{2}$.
However how do you get the solutions for cos(x)=sin(x)
Divide both sides by $\displaystyle \cos{x}$.

So $\displaystyle \tan{x} = 1$.