Solve for theta

**reiward** · October 20th 2009, 01:15 AM

Write all positive values within the interval of 0 degrees < $\theta$ < 270 degrees

$1 - sec^{2} 2\theta - 3tan 2\theta = 0$

**mr fantastic** · October 20th 2009, 02:10 AM

Originally Posted by reiward

Write all positive values within the interval of 0 degrees < $\theta$ < 270 degrees

$1 - sec^{2} 2\theta - 3tan 2\theta = 0$

Substitute $\sec^2 (2 \theta) = \tan^2 (2 \theta) + 1$ , simplify and solve the resulting simple trig equation.

**reiward** · October 20th 2009, 02:21 AM

Originally Posted by mr fantastic

Substitute $\sec^2 (2 \theta) = \tan^2 (2 \theta) + 1$ , simplify and solve the resulting simple trig equation.

$<br /> 1 - sec^{2} 2\theta - 3tan 2\theta = 0$

$<br /> 1 - (\tan^2 (2 \theta) + 1) - 3tan 2\theta = 0$

$\tan^2 (2 \theta) - 3tan 2\theta = 0$

Im stuck. What do I factor it to?

**mr fantastic** · October 20th 2009, 02:30 AM

Originally Posted by reiward

$<br /> 1 - sec^{2} 2\theta - 3tan 2\theta = 0$

$<br /> 1 - (\tan^2 (2 \theta) + 1) - 3tan 2\theta = 0$

$\tan^2 (2 \theta) - 3tan 2\theta = 0$ Mr F says: This is wrong. There is a careless mistake in signs.

Im stuck. What do I factor it to?

Factorise. Note that $\tan (2 \theta)$ is a common factor. Then use the Null Factor Law to get two simple trig equations. Solve them.

**reiward** · October 20th 2009, 02:43 AM

Originally Posted by mr fantastic

Substitute $\sec^2 (2 \theta) = \tan^2 (2 \theta) + 1$ , simplify and solve the resulting simple trig equation.

Originally Posted by mr fantastic

Factorise. Note that $\tan (2 \theta)$ is a common factor. Then use the Null Factor Law to get two simple trig equations. Solve them.

Oh okay.

$-\tan^2 (2 \theta) - 3tan 2\theta = 0$

Can I make that to $\tan^2 (2 \theta) + 3tan 2\theta = 0$ ?

If so, would the factor be $\tan(2 \theta) [tan + 3]= 0$ ?

**mr fantastic** · October 20th 2009, 02:47 AM

Originally Posted by reiward

Oh okay.

$-\tan^2 (2 \theta) - 3tan 2\theta = 0$

Can I make that to $\tan^2 (2 \theta) + 3tan 2\theta = 0$ ?

If so, would the factor be $\tan(2 \theta) [tan + 3]= 0$ ?

Yes.
Yes.

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