Trigonometric Inequalities and Functions

This video tutorial covers solving trigonometric inequalities, focusing on AP pre-calculus topic 3.10. It demonstrates solving inequalities involving cosine and sine using sign charts and critical values. The video also explains solving quadratic trigonometric inequalities by factoring. Key concepts include understanding the unit circle, reference angles, and the zero product property.

What is the main topic of this video?

• Graphing linear functions

• Solving trigonometric inequalities

• Solving algebraic equations

• Calculating derivatives

Why is it important to memorize trigonometric facts?

• To solve trigonometric inequalities efficiently

• To understand calculus concepts

• To solve algebraic equations

• To graph functions accurately

What is the first step in solving the inequality 2cos(θ)sin(θ) + 1 < 0?

• Find the derivative

• Use the zero product property

• Graph the function

• Create a sign chart

In which quadrants is cosine positive?

• Quadrants 1 and 4

• Quadrants 2 and 3

• Quadrants 1 and 2

• Quadrants 3 and 4

What is the reference angle for cosine equal to 1/2?

• π/4

• π/2

• π/3

• π/6

What is the critical value for sin(θ) + 1 = 0?

• π

• 3π/2

• π/2

• 2π

What is the purpose of a sign chart in solving inequalities?

• To graph the function

• To determine where the function is positive or negative

• To calculate the integral

• To find the derivative

What is the solution set for the inequality 2cos(θ)sin(θ) + 1 < 0?

• (0, π/3) ∪ (5π/3, 2π)

• (π/3, 3π/2) ∪ (3π/2, 5π/3)

• (0, 2π)

• (π/3, 5π/3)

What is the first step in solving the inequality sin^2(θ) * 2cos(θ) > 0?

• Find the derivative

• Graph the function

• Use the zero product property

• Create a sign chart

What is the reference angle for cosine equal to √2/2?

• π/2

• π/6

• π/3

• π/4