# Thread: help solving the equation

1. ## help solving the equation

hi wasnt sure whether the two questions should be together or seperate sorry if they were meant to got together

solve the equation 3 sec^2 pheta +7= 11 tan pheta giving all values of x to 3sf in the interval 0<pheta<2pi

sorry for the bad setting out dont no how to get pheta and pi signs

thanks for any help

2. Originally Posted by mannilea
hi wasnt sure whether the two questions should be together or seperate sorry if they were meant to got together

solve the equation 3 sec^2 pheta +7= 11 tan pheta giving all values of x to 3sf in the interval 0<pheta<2pi

sorry for the bad setting out dont no how to get pheta and pi signs

thanks for any help

Use the identity : $\sec^2 \theta=1+\tan^2 \theta$

3. thanks for the reply what could i word in google to get help on how to use the identity as i have never covered that
thanks for any help

4. Just replace $sec^2(\theta)$ with $1+ tan^2(\theta)$ in your equation.

$3sec^2(\theta)+ 7= 11 tan(\theta)$ becomes
$1+ tan^2(\theta)+ 7= 11 tan(\theta)$

If you do not know how to solve that, replace $tan(theta)$ with "x": $1+ x^2+ 7= 11x$ or $x^2- 11x+ 8= 0$. Can you solve that? Then use the fact that $tan(\theta)= x$ to find $\theta$.

5. Originally Posted by HallsofIvy
Just replace $sec^2(\theta)$ with $1+ tan^2(\theta)$ in your equation.

$3sec^2(\theta)+ 7= 11 tan(\theta)$ becomes
$1+ tan^2(\theta)+ 7= 11 tan(\theta)$

If you do not know how to solve that, replace $tan(theta)$ with "x": $1+ x^2+ 7= 11x$ or $x^2- 11x+ 8= 0$. Can you solve that? Then use the fact that $tan(\theta)= x$ to find $\theta$.
but $3sec^2(\theta) = 3(1+tan^2(\theta)) = 3+3tan^2(\theta)$