Exploring Trigonometric Equations and Inequalities

This video tutorial by Mr. Bruss covers the integration of trigonometry with solving equations. It begins with an introduction to solving trigonometric equations using the unit circle for exact values and calculators for approximate values. The tutorial progresses to solving equations without domain restrictions and using factoring techniques. It also includes graphical solutions and solving inequalities, highlighting the effects of period changes on solutions. The video emphasizes understanding the unit circle, inverse functions, and the importance of domain restrictions.

What is the purpose of restricting the domain to between 0 and 2π in trigonometric equations?

• To limit the number of possible solutions

• To simplify the calculations

• To use only positive angles

• To avoid negative values

When solving the equation 2 sin(x) = -1, what is the next step after isolating sin(x)?

• Add 1 to both sides

• Multiply both sides by 2

• Take the inverse sine of both sides

• Square both sides

What is the inverse sine of -1/2 in the restricted domain of 0 to 2π?

• π/6 and 5π/6

• 7π/6 and 11π/6

• π/4 and 3π/4

• π/3 and 2π/3

Why is it important to use the unit circle when finding exact values for trigonometric equations?

• It provides approximate values

• It helps in visualizing the angles

• It avoids the use of calculators

• It simplifies the calculations

What is the result of taking the inverse tangent of -4 using a calculator?

• 0.325

• -0.325

• 1.325

• -1.325

When factoring the equation 3 sin(θ) - sin(θ) = 0, what is the greatest common factor?

• 3

• 1

• sin(θ)

• θ

In the equation 3 sin(θ) - 1 = 0, what is the value of sin(θ)?

• -3

• 1/3

• -1/3

• 3

What is the solution set for the inequality 4 cos(x) + 1 ≤ -2?

• x ∈ [0, π/2]

• x ∈ [2π/3, 4π/3]

• x ∈ [π/3, 2π/3]

• x ∈ [π/4, 3π/4]

How does changing the period of a trigonometric function affect the number of solutions?

• It makes the solutions more complex

• It does not affect the number of solutions

• It increases the number of solutions

• It decreases the number of solutions

What is the inverse cosine of 0?

• π

• 2π

• 0

• π/2