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5.1, 5.2, & 5.4 Vocabulary

                                    Name: ___________________
                                    Period: __________________
                                    Date: ____________________
Across
Although a graphing utility can be useful in helping verify an identity, you must use algebraic techniques to produce a _____ proof.
You will use an identity to rewrite a trigonometric expression in a form that helps you analyze a ________ motion equation.
The final guideline for verifying trigonometric identities is to always try _________. Even making an attempt that leads to a dead end can provide insight.
When factoring trigonometric expressions, it is helpful to find a _______ polynomial factoring form that fits the expression.
The fourth guideline for verifying trigonometric identities is to try ___________ all terms to sines and cosines if the first three guidelines do not help.
The _________ identities state that tangent is equal to sine divided by cosine, and that cotangent is equal to cosine divided by sine.
Sine, cosecant, tangent, and cotangent are all examples of ___ functions.
You will use trigonometric identities to simplify an expression for the coefficient of ________.
The ___________ Identities state that sine squared plus cosine squared equals one, that one plus tangent squared equals secant squared, and that one plus cotangent squared equals cosine squared.
Verifying trigonometric identities is a useful process when you need to convert a trigonometric expression into a form that is more useful _____________.
In this chapter, you will learn how to use the fundamental __________.
There can be more than one ___ to verify an identity.
The third guideline for verifying trigonometric identities is to look for opportunities to use the ____________ identities.
In this chapter, you will learn how to use the fundamental identities to simplify and _____ trigonometric equations.
Sum and difference formulas can be rewritten as expressions involving only sine or cosine. The resulting formulas are called _________ formulas.
Examples 1 and 2 on pages 375-276 show how sum and difference ________ can enable you to find exact values of trigonometric functions involving sums or differences of special angles.
_________, considered the most eminent of Greek astronomers, was born about 190 B.C. in Nicaea. He is credited with the invention of trigonometry. He also derived the sum and difference formulas.
Cosine and secant are examples of ____ functions.
Trigonometric identities can help you simplify the equation that models the length of a shadow cast by a ______ (a device used to tell time).
Down
The key to _________ and solving equations is the ability to use the fundamental identities and the rules of algebra to rewrite trigonometric expressions.
An equation that is true for all values in the domain of the variable is an _______.
On occasion, it is practical to work with each side of a trigonometric equation __________.
In this chapter, you will learn how to use the fundamental identities to ________ and solve trigonometric equations.
In this chapter, you will learn how to use the fundamental identities to ________ additional trigonometric identities.
Remember that a ___________ equation is an equation that is true for only some of the values in its domain.
In this chapter, you will learn how to use the fundamental identities to ________ trigonometric functions.
Remember that an identity is only true for all real values in the _______ of the variable.
Recall from algebra that _____________ the denominator using conjugates is, on occasion, a powerful simplification technique.
When verifying identities, you may find it useful to write Pythagorean identities in one of their ________ forms on page 359.
Example 7 on page 361 shows powers of trigonometric functions rewritten as more ___________ sums of products of trigonometric functions. This is a common procedure use in calculus.
When verifying trigonometric identities, you cannot use operations such as adding the ____ quantity to each side of the equation or cross multiplication.
The first guideline for verifying trigonometric identities is to work with one side of the equation at a ____.
The ___________ Identities state that sine and cosine are cofunctions, that tangent and cotangent are cofunctions, and that secant and cosecant are cofunctions.
The second guideline for verifying trigonometric identities is to look for opportunities to _______ an expression, add fractions, square a binomial, or create a monomial denominator.
One application of the sum and difference formulas is the analysis of standing waves, such as those that can be produced when plucking a guitar string.
When you verify an identity, you cannot ______ that the two sides of the equation are equal because you are trying to verify that they are equal.
On occasion, factoring or simplifying can best be done by first rewriting the expression in terms of just ___ trigonometric function or in terms of sine and cosine only.
Remember that when adding rational expressions, you must first find the ___.