# Trig Equations

• Dec 17th 2008, 09:18 PM
kukid123
Trig Equations
solve each equation on the internal 0 is greater than equal to theta less than 2pie.

10) (cot theta +1)(csc theta -1/2) = 0
• Dec 17th 2008, 09:34 PM
nzmathman
$(\cot{\theta} + 1)(\csc{\theta} - \frac{1}{2}) = 0$

Solutions will be when $\cot{\theta} = -1$ and when $\csc{\theta} = \frac{1}{2}$.

HOWEVER if $\csc{\theta} = \frac{1}{2}$, this implies $\sin{\theta} = 2$ which is invalid.

So the only solutions are found by solving $\tan{\theta} = -1$ (because if $\cot{\theta} = -1$ then so does $\tan{\theta}$)
• Dec 17th 2008, 09:35 PM
mr fantastic
Quote:

Originally Posted by kukid123
solve each equation on the internal 0 is greater than equal to theta less than 2pie.

10) (cot theta +1)(csc theta -1/2) = 0

Case 1: $\cot \theta + 1 = 0 \Rightarrow \tan \theta = -1$. Now solve this simple equation.

Case 2: $\csc \theta - \frac{1}{2} = 0 \Rightarrow \sin \theta = 2$. Do you think there'll be real solutions here ....?
• Dec 17th 2008, 09:45 PM
kukid123
Case 1: http://www.mathhelpforum.com/math-he...3c491824-1.gif. Can you help on this one? I am not getting the message?

Case 2: http://www.mathhelpforum.com/math-he...e8280665-1.gif. OK so this one is obviously not Valid.
• Dec 17th 2008, 09:54 PM
mr fantastic
Quote:

Originally Posted by kukid123
Case 1: http://www.mathhelpforum.com/math-he...3c491824-1.gif. Can you help on this one? I am not getting the message?

[snip]

Hint: $\tan \frac{3 \pi}{4} = -1$. Now use either the known period of $\tan \theta$ or the symmetry of the unit circle to find the second value of $\theta$.

You're expected to know these things. If you don't, then you should be reviewing earlier work on how to solve basic trig equations involving sin, cos and tan instead of attempting to solve the equations you've been posting.
• Dec 17th 2008, 10:09 PM
kukid123
OK right so the answer would be (-sqrt2/2, sqrt2/2)?
• Dec 18th 2008, 12:10 AM
nzmathman
Right, you know that $\cot{\theta} = -1$, and you should know that $\tan{\theta} = \frac{1}{\cot{\theta}}$. So in this case $\tan{\theta} = \frac{1}{-1} = -1$

You should know how to find the values for $\theta$ in the interval $0 \leq \theta \leq 2\pi$ that satisfy this equation.

You should have $\theta = \left\{ \frac{3\pi}{4},~ \frac{7\pi}{4} \right\}$