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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

2. Solving Trigonometric Equations Using Inverses

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Exercise 50 Page 917

Start by rewriting the equation so that all the terms are on one side. Next, factor the equation and use the Zero Product Property.

$0 + π n$ radians, $1.25 + π n$ radians, for any integer $n$

Practice makes perfect

We will start by rewriting the equation so that all the terms are on one side.Next, we can factor the equation and use the Zero Product Property.

Solving the Equation

Rearrange the equation and factor out common factors. Then use the Zero Product Property.

tan θ sin θ = 3 sin θ

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Simplify

$LHS - 3 sin θ = RHS - 3 sin θ$

tan θ sin θ - 3 sin θ = 0

Factor out $sin θ$

(tan θ - 3) sin θ = 0

Use the Zero Product Property

tan θ - 3 = 0 sin θ = 0 (I) (II)

$(I):$ $LHS + 3 = RHS + 3$

tan θ = 3 sin θ = 0

Let's solve these equations one at a time.

$tan θ = 3$

Let's isolate

θ .

tan θ = 3

$tan^{- 1} (LHS) = tan^{- 1} (RHS)$

θ = tan^{- 1} (3)

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Subchapter links

Lesson Check p.915

Practice and Problem-Solving Exercises p.916-918

Standardized Test Prep p.918

Mixed Review p.918