Lesson 68 of 1524
Trigonometric Identities and Equations
There are multiple ways to represent a trigonometric expression.
Practice this chapterThere are multiple ways to represent a trigonometric expression. Verifying the identities illustrates how expressions can be rewritten to simplify a problem
Graphing both sides of an identity will verify it Simplifying one side of the equation to equal the other side is another method for verifying an identity
even-odd identities — set of equations involving trigonometric functions such that if f ( - x ) = - f ( x ) , the identity is odd, and if f ( - x ) = f ( x ) , the identity is even. quotient identities — pair of identities based on the fact that tangent is the ratio of sine and cosine, and cotangent is the ratio of cosine and sine. double-angle formulas — identities derived from the sum formulas for sine, cosine, and tangent in which the angles are equal. product-to-sum formula — a trigonometric identity that allows the writing of a product of trigonometric functions as a sum or difference of trigonometric functions.
Worked example
What does “even-odd identities” mean in Trigonometric Identities and Equations?
- 1Use the wording this chapter gives for even-odd identities.
- 2The book says: set of equations involving trigonometric functions such that if f ( - x ) = - f ( x ) , the identity is odd, and if f ( - x ) = f ( x ) , the identity is even.
- 3Do not use the meaning of quotient identities. That term means pair of identities based on the fact that tangent is the ratio of sine and cosine, and cotangent is the ratio of cosine and sine.
Result: set of equations involving trigonometric functions such that if f ( - x ) = - f ( x ) , the identity is odd, and if f ( - x ) = f ( x ) , the identity is even
Why. That is the meaning this chapter gives for even-odd identities.
Do not swap even-odd identities and quotient identities. even-odd identities means set of equations involving trigonometric functions such that if f ( - x ) = - f ( x ) , the identity is odd, and if f ( - x ) = f ( x ) , the identity is even. quotient identities means pair of identities based on the fact that tangent is the ratio of sine and cosine, and cotangent is the ratio of cosine and sine.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.