- #1

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sin^2 theta - cos^2 theta is not the same thing as one?

If I had a problem say... 1 + cos^2 theta would that equal to sin^2 theta? Or -sin^2 theta? Thanks

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- Thread starter CrossFit415
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- #1

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sin^2 theta - cos^2 theta is not the same thing as one?

If I had a problem say... 1 + cos^2 theta would that equal to sin^2 theta? Or -sin^2 theta? Thanks

- #2

eumyang

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I'm on mobile so I can't use latex..

sin^2 theta - cos^2 theta is not the same thing as one?[/tex]

No, it isn't.

[tex]\sin^2 \theta + \cos^2 \theta = 1[/tex]

Neither.If I had a problem say... 1 + cos^2 theta would that equal to sin^2 theta? Or -sin^2 theta? Thanks

[tex]1 + \cos^2 \theta = 2 - \sin^2 \theta[/tex]

Do you see why?

- #3

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I don't understand how there is a two there.

- #4

gb7nash

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I don't understand how there is a two there.

Do you understand why [tex]\sin^2 \theta + \cos^2 \theta = 1[/tex] is true?

Once you understand that identity, what do you have to do to the equation to get:

[tex]1 + \cos^2 \theta = 2 - \sin^2 \theta[/tex]

?

- #5

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1 + \cos^2 \theta = 2 - \sin^2 \theta

[/tex]

Think of it this way. If you start from the fundamental pythag. identity:

sin²x + cos²x = 1

You can subtract the sine over so you get:

cos²x = 1-sin²x

Now, 2-sin²x is really the same as

1+1-sin²x

isn't it?

Can you see where I am going with this?

- #6

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1 + \cos^2 \theta = 2 - \sin^2 \theta

[/tex]

Think of it this way. If you start from the fundamental pythag. identity:

sin²x + cos²x = 1

You can subtract the sine over so you get:

cos²x = 1-sin²x

Now, 2-sin²x is really the same as

1+1-sin²x

isn't it?

Can you see where I am going with this?

I understand how we move the sine to the right. That would equal to 1-sin²x. But where did the 1 come from that made it 1+1 = 2? All I see is 1-sin²x. So -sin²x can also have a 1 infront of it? Sorry for the frustration.

So If I do the same thing for cos²x, then

sin²x = 1-cos²x

sin²x = 1+1-cos²x

sin²x = 2-cos²x ?

- #7

vela

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- #8

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A great deal of times, when a trig identity has something that would use the pyth. identity, the multiplication of conjugates is needed to get it into the right form.

- #9

eumyang

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The 1 came from the expression thatI understand how we move the sine to the right. That would equal to 1-sin²x. But where did the 1 come from that made it 1+1 = 2? All I see is 1-sin²x. So -sin²x can also have a 1 infront of it? Sorry for the frustration.

All we are doing is replacing the cos

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