Why Do Negative Angles Have Opposite Trig Identities?

In summary, the conversation discusses the concept of sine, cosine, and tangent functions, specifically when applied to negative angles. The person mentions that their book did not provide a clear explanation and they do not understand how it relates to negative angles. They suggest looking at the unit circle for a better understanding.
  • #1
Miike012
1,009
0
My book was proving that..
sin(-x) = -sin(x)
tan(-x) = -tan(x)
cos(-x) = cos(x)

.. I posted an attachment of the books explanation.. I just don't understand how their explanation has anything to do with sin of a negative angle equaling sin of an angle times negative one, the same goes for tan and cos...
 

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  • #2
Your book should have explained the sine and cosine functions in terms of the unit circle. The oddness of the sine function and the evenness of the cosine function are probably a bit easier to understand if you see the picture. See here, about the middle of the page.
 

1. What are odd and even trig identities?

Odd and even trig identities refer to the properties of trigonometric functions that determine how they behave when the angle is negative or when it is reflected across the y-axis.

2. What is an odd trig identity?

An odd trig identity is a function that satisfies the property f(-x) = -f(x), meaning that when the angle is negative, the function's value will be the opposite of what it would be for a positive angle. Examples of odd trig functions include sine and tangent.

3. What is an even trig identity?

An even trig identity is a function that satisfies the property f(-x) = f(x), meaning that the function's value remains the same when the angle is reflected across the y-axis. Examples of even trig functions include cosine and secant.

4. How are odd and even trig identities used in solving trigonometric equations?

When solving trigonometric equations, identifying whether the function is odd or even can be helpful in simplifying the equation. For odd functions, the negative angle can be factored out and for even functions, the absolute value of the angle can be used.

5. Can a function be both odd and even?

No, a function cannot be both odd and even. A function can only satisfy one of the properties, and if it satisfies both, it is considered an identity function.

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