Doubt about trigonometry Identities from sin α

In summary, the trigonometry identities can be derived from the sine and cosine functions, which have maximum amplitude on the unit circle. It may be helpful to think about the unit circle and realize there are two quadrants where the sine function is positive. Once you have the two angles, you can add ##\pm 2\pi## to each.
  • #1
Ray9927
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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?
 
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  • #2
Ray9927 said:
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
 
  • #3
Ray9927 said:
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.

[Edit] I see SteamKing posted while I was still editing...
 

What are the basic trigonometric identities?

The basic trigonometric identities are sin^2 α + cos^2 α = 1, tan α = sin α / cos α, and cot α = cos α / sin α. These identities are used to solve trigonometric equations and simplify expressions.

How do I prove a trigonometric identity?

To prove a trigonometric identity, you must manipulate the expression using known identities and algebraic techniques until it is equivalent to the other side of the identity. This can involve using trigonometric identities, factoring, and simplifying fractions.

What are the Pythagorean identities?

The Pythagorean identities are sin^2 α + cos^2 α = 1 and tan^2 α + 1 = sec^2 α. These identities are based on the Pythagorean theorem and are used to simplify trigonometric expressions and solve equations.

How do I use trigonometric identities to solve equations?

To solve equations involving trigonometric identities, you can first manipulate the expression using known identities to simplify it. Then, use algebraic techniques to isolate the variable and solve for its value. Finally, check your answer by plugging it back into the original equation.

What is the difference between a trigonometric identity and an equation?

A trigonometric identity is an equation that is true for all values of the variable, whereas a trigonometric equation is only true for specific values of the variable. Trigonometric identities are used to manipulate and simplify expressions, while trigonometric equations are used to solve for the value of the variable.

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