Grade 11 Trigonometric Identites Questions

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obocher

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I am trying to teach myself grade 11 Trigonometry, and I find I would have spent less time on this if I had paid attention in class, can someone help me with two things. Both are about Trigonometric Identities.

1) What is an equivalent expression to cos^2x-1, and what are the steps to getting that?

2) When I am asked to prove that the L.S. = R.S. what steps should I be taking and showing?

Thanks in advance.
 
obocher said:
I am trying to teach myself grade 11 Trigonometry, and I find I would have spent less time on this if I had paid attention in class, can someone help me with two things. Both are about Trigonometric Identities.

1) What is an equivalent expression to cos^2x-1, and what are the steps to getting that?

\(\displaystyle \cos^2(x) \, - \, 1 \, = \cos^2(x) \, - \, [\cos^2(x) \, + \, \sin^2(x)] \, = - \, \sin^2(x)\)


2) When I am asked to prove that the L.S. = R.S. what steps should I be taking and showing?----That depends on the particular problem.

Thanks in advance.
Click to expand...
 
obocher said:
sin(theta)cos(theta)tan(theta)-1 = -cos^2(theta)

How about that one?
Click to expand...

In this - I would start with LHS (almost obvious - RHS has only one term - very little chance of manipulation)

Convert tan(theta) in terms of sin(theta) and cos(theta)

Show us what you get....
 
\(\displaystyle \sin^2x + \cos^2x = 1\)

Manipulate to get
\(\displaystyle \cos^2x-1\)
on one side of equation.
 
obocher said:
I find I would have spent less time on this if I had paid attention in class
Click to expand...

I hope this has caused that old "light bulb" to come on. Things are discussed in class to help you when you are trying to do problems on your own....if that weren't the purpose, why would teachers spend all of those class hours on explanation and discussion?

Sorry....you created this problem for yourself.
 
Okay, how about this one, Prove this equation is an identity.
sin^2(theta)(cos^2(theta)/sin^2(theta) +1) = 1
 
\(\displaystyle \sin^2\theta\left(\frac{\cos^2\theta}{\sin^2\theta}+1\right)=1\)

Pretty obvious.
 
obocher said:
Okay, how about this one, Prove this equation is an identity.
sin^2(theta)(cos^2(theta)/sin^2(theta) +1) = 1
Click to expand...

Please start a new thread (new topic) with new problem.
 
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