I need help understanding trigonometric identities

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
Wags
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Joined: Fri Oct 22, 2010 12:38 am
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I need help understanding trigonometric identities

Hello, I'm a sophomore in high school that started Algebra 2 & Trigonometry this year, so I am a first year student of trig with little experience with it. I do not understand the trigonometric identities. I have a list of trigonometric identities in my notes, but I don't know how to use them in order to solve a problem.

Example from my homework:

Solve for values of $\theta$ between 0o and 90o.
If Cos$\theta$ =$\frac{5}{13}$, find Sin$\theta$.

Where exactly would I start with this equation? I was thinking I would use the Pythagorean identity "Sin2$\theta$+Cos2$\theta$=1"; however, I am not sure.

How would I solve this problem if the value of $\theta$ is between 180o and 270o. What about between 270o and 360o?

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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Re: I need help understanding trigonometric identities

Hello, I'm a sophomore in high school that started Algebra 2 & Trigonometry this year, so I am a first year student of trig with little experience with it. I do not understand the trigonometric identities. I have a list of trigonometric identities in my notes, but I don't know how to use them in order to solve a problem.

Example from my homework:

Solve for values of $\theta$ between 0o and 90o.
If Cos$\theta$ =$\frac{5}{13}$, find Sin$\theta$.

Where exactly would I start with this equation? I was thinking I would use the Pythagorean identity "Sin2$\theta$+Cos2$\theta$=1"; however, I am not sure.
you can use that.

trgreene42
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Joined: Tue Nov 30, 2010 10:51 am
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Re: I need help understanding trigonometric identities

sin^2+cos^2=1
thus
If cos theta= (5/13)

sin^2+(5/13)^2=1

sin^2+(25/169)=1

sin^2=(169/169)-(25/169)

sin^2=(144/169)

sin theta= sqrt of (144/169)

sin theta= (12/13)

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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Re: I need help understanding trigonometric identities

another way is to notice that $\cos(\theta)$ is adj/hyp on a right triangle

this creates a 5,12,13 triangle: adj=5, opp=12, hyp=13

$\sin(\theta)$ which is opp over hyp is therefore $\frac{12}{13}$