Trigonometric Equations and Functions

This video tutorial covers solving trigonometric equations involving inverse functions. It begins with an introduction to the topic, followed by detailed solutions to three problems. The first problem involves solving an equation with inverse sine, the second problem focuses on an arctan equation, and the third problem uses inverse sine and cosine. The video emphasizes understanding the properties of inverse functions and their application in solving equations.

What is the first step in solving a trigonometric equation involving inverse sine?

• Add a constant to both sides

• Multiply both sides by a constant

• Take the cosine of both sides

• Isolate the sine function

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CCSS.HSF.TF.B.7

When solving for x in the interval from 0 to 2π, why is it important to consider the sine function's positivity in different quadrants?

• To find the maximum value of sine

• To determine the period of the sine function

• To identify all possible solutions for x

• To calculate the derivative of sine

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CCSS.HSF.TF.B.7

How can you verify the solutions of a trigonometric equation using a graphing calculator?

• By ensuring the solutions match the expected value

• By calculating the derivative of the solutions

• By comparing the solutions to a sine table

• By checking if the solutions are integers

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CCSS.HSF.TF.B.7

What is the result of taking the tangent of both sides of the equation 4 arctan x = π?

• x = tan(π/4)

• x = arctan(π/4)

• x = 1/√2

• x = π/4

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CCSS.HSF.TF.A.2

What is the significance of the angle 45 degrees in the context of tangent functions?

• It is the angle where tangent equals 0

• It is the angle where tangent equals 1

• It is the angle where tangent equals -1

• It is the angle where tangent is undefined

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CCSS.HSF.TF.B.7

In the context of solving trigonometric equations, what does the inverse sine of a ratio represent?

• A constant value

• The cosine of an angle

• The tangent of an angle

• An angle with a specific sine ratio

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CCSS.8.G.B.8

What is the purpose of using the Pythagorean theorem in solving trigonometric equations involving right triangles?

• To determine the angle of elevation

• To find unknown side lengths

• To find the hypotenuse of the triangle

• To calculate the area of the triangle

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CCSS.8.EE.A.2

Why is it unnecessary to consider negative values when finding the square root of a side length in a right triangle?

• Because the cosine function is always negative

• Because negative values are not real numbers

• Because side lengths are always positive

• Because the sine function is always positive

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CCSS.HSG.SRT.C.6

What is the cosine of an angle in a right triangle with an opposite side of 3 and a hypotenuse of 7?

• 3/7

• 7/3

• √40/7

• 2√10/7

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CCSS.HSF.TF.B.7

How does the inverse sine function help in solving trigonometric equations?

• It calculates the derivative of sine

• It converts angles to radians

• It provides the maximum value of sine

• It helps find angles with a given sine value

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CCSS.HSF.TF.B.7