I need help understanding trigonometric identities

[Wags]

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 between 0^o and 90^o.
If Cos =, find Sin.

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

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

[Martingale]

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 between 0^o and 90^o.
If Cos =, find Sin.

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

you can use that.

[trgreene42]

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]

another way is to notice that is adj/hyp on a right triangle



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


which is opp over hyp is therefore