castilloxc
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- Nov 29, 2007
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Simplify:
csc(pheta)
cot(pheta
how do you do this???
csc(pheta)
cot(pheta
how do you do this???
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how do you do basic trigonometric identities
- Thread starter castilloxc
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nycfunction
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- Nov 28, 2007
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castilloxc said:Simplify:
csc(pheta)
cot(pheta
how do you do this???
I think you meant to type theta not pheta.
Theta is one of the letters of the Greek alphabet.
Anyway, we have this: csc(theta)/cot(theta)
The best thing to do when dealing with trig identities is to change everything that is given to sine and cosine.
I do not want to keep typing the word theta. So, let t = theta, for short.
Got it?
csc(t) = 1/sin(t)
cot(t) = cos(t)/sin(t)
We have now formed a complex fraction:
1/sin(t) divided by cos(t)/sin(t) = 1/cos(t) = sec(t)
Simplify:
\(\displaystyle \frac{\csc\theta}{\cot\theta}=\frac{\frac{1}{\sin\theta}}{\frac{\cos\theta}{\sin\theta}}=\frac{\frac{1}{\sin\theta}}{\frac{\cos\theta}{\sin\theta}}\cdot\frac{\frac{\sin\theta}{1}}{\frac{\sin\theta}{1}}=\frac{1}{\cos\theta}\) or \(\displaystyle \sec\theta\)
Of course, this is not an identity. An identity is an equation (it has an equal sign) that is true for all values of the variable. What you have given here is an expression and we have turned it into another expression that is equal to the original expression but is in a less complex form.
\(\displaystyle \frac{\csc\theta}{\cot\theta}=\frac{\frac{1}{\sin\theta}}{\frac{\cos\theta}{\sin\theta}}=\frac{\frac{1}{\sin\theta}}{\frac{\cos\theta}{\sin\theta}}\cdot\frac{\frac{\sin\theta}{1}}{\frac{\sin\theta}{1}}=\frac{1}{\cos\theta}\) or \(\displaystyle \sec\theta\)
Of course, this is not an identity. An identity is an equation (it has an equal sign) that is true for all values of the variable. What you have given here is an expression and we have turned it into another expression that is equal to the original expression but is in a less complex form.