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7th Edition

James Stewart + 2 others

Publisher: Brooks Cole

ISBN: 9781305071759

Chapter 7.4, Problem 50E

Textbook Problem

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**Solving Trigonometric Equations by Factoring** Solve the given equation.

**50.** 3 tan^{3}*θ* = tan *θ*

To determine

**To solve:** The equation

Given equation can be rewritten as follows,

For the given equation either

Consider

That is,

Thus, the solutions of the equation

Precalculus: Mathematics for Calculus (Standalone Book)

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Solving Trigonometric Equations by Factoring Solve...Ch. 7.4 - Solving Trigonometric Equations by Factoring Solve...Ch. 7.4 - Solving Trigonometric Equations by Factoring Solve...Ch. 7.4 - Solving Trigonometric Equations by Factoring Solve...Ch. 7.4 - Solving Trigonometric Equations by Factoring Solve...Ch. 7.4 - Solving Trigonometric Equations by Factoring Solve...Ch. 7.4 - Solving Trigonometric Equations by Factoring Solve...Ch. 7.4 - Solving Trigonometric Equations by Factoring Solve...Ch. 7.4 - Solving Trigonometric Equations by Factoring Solve...Ch. 7.4 - Refraction of Light It has been observed since...Ch. 7.4 - Total Internal Reflection When light passes from a...Ch. 7.4 - Phases of the Moon As the moon revolves around the...Ch. 7.4 - DISCUSS WRITE: Equations and Identities Which of...Ch. 7.5 - We can use identities to help us solve...Ch. 7.5 - We can use identities to help us solve...Ch. 7.5 - Solving Trigonometric Equations by Using...Ch. 7.5 - Solving Trigonometric Equations by Using...Ch. 7.5 - 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Using Addition or Subtraction Formulas Use an...Ch. 7.5 - Using Double- or Half-Angle Formulas Use a Double-...Ch. 7.5 - Using Double- or Half-Angle Formulas Use a Double-...Ch. 7.5 - Using Double- or Half-Angle Formulas Use a Double-...Ch. 7.5 - Using Double- or Half-Angle Formulas Use a Double-...Ch. 7.5 - Using Double- or Half-Angle Formulas Use a Double-...Ch. 7.5 - Using Double- or Half-Angle Formulas Use a Double-...Ch. 7.5 - Using Double- or Half-Angle Formulas Use a Double-...Ch. 7.5 - Using Double- or Half-Angle Formulas Use a Double-...Ch. 7.5 - Using Double- or Half-Angle Formulas Use a Double-...Ch. 7.5 - Using Double- or Half-Angle Formulas Use a Double-...Ch. 7.5 - Using Sum-to-Product Formulas Solve the equation...Ch. 7.5 - Using Sum-to-Product Formulas Solve the equation...Ch. 7.5 - Using Sum-to-Product Formulas Solve the equation...Ch. 7.5 - Using Sum-to-Product Formulas Solve the equation...Ch. 7.5 - Solving Trigonometric Equations Graphically Use a...Ch. 7.5 - Solving Trigonometric Equations Graphically Use a...Ch. 7.5 - Solving Trigonometric Equations Graphically Use a...Ch. 7.5 - Solving Trigonometric Equations Graphically Use a...Ch. 7.5 - Solving Trigonometric Equations Graphically Use a...Ch. 7.5 - Solving Trigonometric Equations Graphically Use a...Ch. 7.5 - Equations Involving Inverse Trigonometric...Ch. 7.5 - Equations Involving Inverse Trigonometric...Ch. 7.5 - Range of a Projectile If a projectile is fired...Ch. 7.5 - Damped Vibrations The displacement of a spring...Ch. 7.5 - Hours of Daylight In Philadelphia the number of...Ch. 7.5 - Belts and Pulleys A thin belt of length L...Ch. 7.5 - DISCUSS: A Special Trigonometric Equation What...Ch. 7 - What is an identity? What is a trigonometric...Ch. 7 - (a) State the Pythagorean identities. (b) Use a...Ch. 7 - (a) State the reciprocal identities for cosecant,...Ch. 7 - (a) How do you prove an identity? (b) Prove the...Ch. 7 - (a) State the Addition and Subtraction Formulas...Ch. 7 - (a) State the formula for A sin x + B cos x. (b)...Ch. 7 - (a) State the Double-Angle Formula for Sine and...Ch. 7 - (a) State the formulas for lowering powers of sine...Ch. 7 - (a) State the Half-Angle Formulas for Sine and...Ch. 7 - (a) State the Product-to-Sum Formula for the...Ch. 7 - (a) State the Sum-to-Product Formula for the sum...Ch. 7 - What is a trigonometric equation? How do we solve...Ch. 7 - Proving Identities Verify the identity. 1. sin ...Ch. 7 - Proving Identities Verify the identity. 2. (sec ...Ch. 7 - Proving Identities Verify the identity. 3. cos2x...Ch. 7 - Proving Identities Verify the identity. 4....Ch. 7 - Proving Identities Verify the identity. 5....Ch. 7 - Proving Identities Verify the identity. 6....Ch. 7 - Proving Identities Verify the identity. 7....Ch. 7 - Proving Identities Verify the identity. 8. (1 tan...Ch. 7 - Proving Identities Verify the identity. 9. sin2x...Ch. 7 - Proving Identities Verify the identity. 10. (tan x...Ch. 7 - Proving Identities Verify the identity. 11....Ch. 7 - Proving Identities Verify the identity. 12....Ch. 7 - Proving Identities Verify the identity. 13....Ch. 7 - Proving Identities Verify the identity. 14....Ch. 7 - Proving Identities Verify the identity. 15....Ch. 7 - Proving Identities Verify the identity. 16....Ch. 7 - Proving Identities Verify the identity. 17....Ch. 7 - Proving Identities Verify the identity. 18. (cos x...Ch. 7 - Proving Identities Verify the identity. 19....Ch. 7 - Proving Identities Verify the identity. 20....Ch. 7 - Proving Identities Verify the identity. 21....Ch. 7 - Proving Identities Verify the identity. 22. sin(x...Ch. 7 - Checking Identities Graphically (a) Graph f and g....Ch. 7 - Checking Identities Graphically (a) Graph f and g....Ch. 7 - Checking Identities Graphically (a) Graph f and g....Ch. 7 - Checking Identities Graphically (a) Graph f and g....Ch. 7 - Determining Identities Graphically (a) Graph the...Ch. 7 - Determining Identities Graphically (a) Graph the...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Solving Trigonometric Equations Solve the equation...Ch. 7 - Range of a Projectile If a projectile is fired...Ch. 7 - Displacement of a Shock Absorber The displacement...Ch. 7 - Value of Expressions Find the exact value of the...Ch. 7 - Value of Expressions Find the exact value of the...Ch. 7 - Value of Expressions Find the exact value of the...Ch. 7 - Value of Expressions Find the exact value of the...Ch. 7 - Value of Expressions Find the exact value of the...Ch. 7 - Value of Expressions Find the exact value of the...Ch. 7 - Value of Expressions Find the exact value of the...Ch. 7 - Value of Expressions Find the exact value of the...Ch. 7 - Value of Expressions Find the exact value of the...Ch. 7 - Value of Expressions Find the exact value of the...Ch. 7 - Evaluating Expressions Involving Trigonometric...Ch. 7 - Evaluating Expressions Involving Trigonometric...Ch. 7 - Evaluating Expressions Involving Trigonometric...Ch. 7 - Evaluating Expressions Involving Trigonometric...Ch. 7 - Evaluating Expressions Involving Trigonometric...Ch. 7 - Evaluating Expressions Involving Trigonometric...Ch. 7 - Evaluating Expressions Involving Inverse...Ch. 7 - Evaluating Expressions Involving Inverse...Ch. 7 - Expressions Involving Inverse Trigonometric...Ch. 7 - Expressions Involving Inverse Trigonometric...Ch. 7 - Expressions Involving Inverse Trigonometric...Ch. 7 - Viewing Angle of a Tower A 380-ft-tall building...Ch. 7 - Verify each identity. 1. tan sin + cos = secCh. 7 - Verify each identity. 2. tanx1cosx=cscx(1+secx)Ch. 7 - Verify each identity. 3. 2tanx1+tan2x=sin2xCh. 7 - Verify each identity. 4. sinxtan(x2)=1cosxCh. 7 - Verify each identity. 5. 2 sin2(3x) = 1 cos(6x)Ch. 7 - Verify each identity. 6. cos 4x = 1 8 sin2x + 8...Ch. 7 - Verify each identity. 7. (sin(x2)+cos(x2))2=1+sinxCh. 7 - Verify each identity. 8. Let x = 2 sin , /2 /2....Ch. 7 - Find the exact value of each expression. (a) sin 8...Ch. 7 - For the angles and in the figures, find cos( +...Ch. 7 - Write sin 3x cos 5x as a sum of trigonometric...Ch. 7 - Write sin 2x sin 5x as a product of trigonometric...Ch. 7 - If sin=45 and is in Quadrant III, find tan(/2).Ch. 7 - Solve each trigonometric equation in the interval...Ch. 7 - Solve each trigonometric equation in the interval...Ch. 7 - Solve each trigonometric equation in the interval...Ch. 7 - Solve each trigonometric equation in the interval...Ch. 7 - Solve each trigonometric equation in the interval...Ch. 7 - Solve each trigonometric equation in the interval...Ch. 7 - Solve each trigonometric equation in the interval...Ch. 7 - Find the exact value of cos(2tan1940).Ch. 7 - Rewrite the expression as an algebraic function of...Ch. 7 - Wave on a Canal A wave on the surface of a long...Ch. 7 - Wave in a Rope Traveling waves are generated at...Ch. 7 - Traveling Wave A traveling wave is graphed at the...Ch. 7 - Traveling Wave A traveling wave has period 2/3,...Ch. 7 - Standing Wave A standing wave with amplitude 0.6...Ch. 7 - Standing Wave A standing wave has maximum...Ch. 7 - Vibrating String When a violin string vibrates,...Ch. 7 - Waves in a Tube Standing waves in a violin string...

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