help solving the equation

**mannilea** · September 9th 2009, 06:07 AM

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

**mathaddict** · September 9th 2009, 06:11 AM

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 : $\sec^2 \theta=1+\tan^2 \theta$

**mannilea** · September 9th 2009, 06:41 AM

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

**HallsofIvy** · September 9th 2009, 11:13 AM

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 $\theta$ .

**e^(i*pi)** · September 9th 2009, 11:48 AM

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

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