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Lesson 1104 of 1524

Trigonometric Identities and Equations

There are multiple ways to represent a trigonometric expression.

Practice this chapter

There 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

damped harmonic motion — oscillating motion that resembles periodic motion and simple harmonic motion, except that the graph is affected by a damping factor, an energy dissipating influence on the…. 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.

Be able to use key points to graph a sinusoidal function. The five key points include the minimum and maximum values and the midline values.

Worked example

What does “damped harmonic motion” mean in Trigonometric Identities and Equations?

  1. 1Use the wording this chapter gives for damped harmonic motion.
  2. 2The book says: oscillating motion that resembles periodic motion and simple harmonic motion, except that the graph is affected by a damping factor, an energy dissipating influence on the….
  3. 3Do not use the meaning of even-odd identities. That term 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.

Result: oscillating motion that resembles periodic motion and simple harmonic motion, except that the graph is affected by a damping factor, an energy dissipating influence on the…

Why. That is the meaning this chapter gives for damped harmonic motion.

Do not swap damped harmonic motion and even-odd identities. damped harmonic motion means oscillating motion that resembles periodic motion and simple harmonic motion, except that the graph is affected by a damping factor, an energy dissipating influence on the…. 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.

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.