Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I know that $\cot\theta = 4/3$ how do I find $\csc\theta$?

I tried to do $\csc^2\theta - \cot^2\theta = 1$

This gives me $\csc^2\theta = 1 + \cot^2\theta$

this gives $csc^2\theta = 9/9 + 16/9 = 27/9 = \sqrt{3}$

is this wrong? My book gives the answer as $5/3$

I can never go more than $2$ homework problems without getting stuck.

share|improve this question
3  
You did everthing right, but 9+16 = 25 not 27 –  crasic Jun 28 '11 at 22:02

3 Answers 3

up vote 2 down vote accepted

I don't see what is your problem here... You know that $csc^2 x= 1+\cot^2 x=1+\frac{16}{9}=\frac{25}{9}$. From here, you get $\csc x=\frac{5}{3}$. It's pure algebra. Just look at what you have and where do you want to get, and as I said, do not rush with computations, since I notice you make very many elementary mistakes.

share|improve this answer
    
Yeah I checked my work about 12 times, I am attempting to review 14 sections before tomorrow to catch up since I am so far behind in class. I will likely get two or three done at this rate. –  Adam Jun 28 '11 at 22:06
    
Well, since you had time to check 12 times, try and slow down your computation and writing speed, and think very well every step. Don't skip anything as being too easy. –  Beni Bogosel Jun 28 '11 at 22:10
    
@Adam as I pointed out in my comment, even though you checked 12 times you missed the clear arithmetic error –  crasic Jun 28 '11 at 22:13

If $\cot{(x)} = 4/3$, then we have this picture

<

                 /|
                / |  3
           5   /  |
              /   |
             x-----
               4

Now compute.

share|improve this answer
    
It would help a bit more simply by being clear about which angle is $\theta$, so as not to confuse Adam...I just added the angle "x" to illustrate your relation. –  amWhy Jun 28 '11 at 22:50

Do you know "Soh-Cah-Toa"? That is sine is the opposite side over hypoteneuse, cosine adjacent over hypoteneuse, and tangent is opposite over adjacent. Then cotangent will be adjacent over hypoteneuse. Therefore you have a right triangle where the side adjacent to your angle is 4 and the side across from your angle is 3. Pythagorean Theorem says the hypoteneuse is 5. Therefore cosecant, which is hypoteneuse over opposite is 5/3.

share|improve this answer
    
I have absolutely no idea how you figured out that it was a right triangle. –  Adam Jun 28 '11 at 22:05
    
@Adam trig functions represent relations between the sides of a right triangle. Excepting some corner cases (like $\theta = \frac{\pi}{2}$) you can always construct a right triangle that "represents" the trig relation. –  crasic Jun 28 '11 at 22:15

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.