# Doubt about trigonometry Identities from sin α

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Hi all! I'm Ray and I'm new to this community, it's a pleasure!

I'm trying to resolve a trigonometry exercise where I have to calculate the trigonometry Identities of a right triangle but in the specifications they don't show me any common data (hypotenuse or cathethus values), they just leave me a sen α= √3/ 2

I know how to calculate the identities parting from the main two values, maybe the hypotenuse and one of the cathethus, then using the The Pythagorean Theorem to isolate the remaining variable, and finally reflecting the values in the identities formules (sen, cos, tan...) to finish the excercise but, this is completely new for me...

What should I do to proceed with this type of excercise? should I use the sen formule: Opposite/ hypotenuse with √3/ 2 to obtain the first values? i mean √3= Opposite and 2= hypotenuse?

SteamKing
Staff Emeritus
Homework Helper
Hi all! I'm Ray and I'm new to this community, it's a pleasure!

I'm trying to resolve a trigonometry exercise where I have to calculate the trigonometry Identities of a right triangle but in the specifications they don't show me any common data (hypotenuse or cathethus values), they just leave me a sen α= √3/ 2

I know how to calculate the identities parting from the main two values, maybe the hypotenuse and one of the cathethus, then using the The Pythagorean Theorem to isolate the remaining variable, and finally reflecting the values in the identities formules (sen, cos, tan...) to finish the excercise but, this is completely new for me...

What should I do to proceed with this type of excercise? should I use the sen formule: Opposite/ hypotenuse with √3/ 2 to obtain the first values? i mean √3= Opposite and 2= hypotenuse?
Trig functions are usually developed for the unit circle:

http://www.regentsprep.org/regents/math/algtrig/att5/unitcircle.gif

The sine and cosine functions have maximum amplitude of 1, so the unit circle works fine for these types of calculations.

In the circle above, sin (θ) = y and cos (θ) = x and the Pythagorean relation is x2 + y2 = 1

LCKurtz
Homework Helper
Gold Member
Hi all! I'm Ray and I'm new to this community, it's a pleasure!

I'm trying to resolve a trigonometry exercise where I have to calculate the trigonometry Identities of a right triangle but in the specifications they don't show me any common data (hypotenuse or cathethus values), they just leave me a sen α= √3/ 2

I know how to calculate the identities parting from the main two values, maybe the hypotenuse and one of the cathethus, then using the The Pythagorean Theorem to isolate the remaining variable, and finally reflecting the values in the identities formules (sen, cos, tan...) to finish the excercise but, this is completely new for me...

What should I do to proceed with this type of excercise? should I use the sen formule: Opposite/ hypotenuse with √3/ 2 to obtain the first values? i mean √3= Opposite and 2= hypotenuse?

Well, yes. But I would think about the unit circle and realize there are two quadrants where the sine function is positive. So you get two different angles and then you can add ##\pm 2\pi## to each.

 I see SteamKing posted while I was still editing...