Trigonometric Functions and Quadrants

This video tutorial covers solving basic trigonometric inequalities, focusing on sine and cosine functions. It explains how to find theta values within a given interval where these functions meet specific inequality conditions. The video also demonstrates how to compare trigonometric functions to determine solution sets and provides interval notation and inequality representations. The tutorial concludes with a call to action for further learning resources.

What is the main focus of this video tutorial?

• Solving quadratic equations

• Understanding algebraic expressions

• Practicing basic trigonometric inequalities

• Learning about calculus derivatives

Which interval is considered for finding values of θ where sin(θ) is less than -2?

• 0 to π/2

• π to 2π

• 0 to π

• 0 to 2π

In which quadrants is sin(θ) negative?

• First and second

• Second and third

• Third and fourth

• First and fourth

What is the reference angle for sin(θ) = -1/2?

• π/4

• π/3

• π/6

• π/2

Which angles are solutions for sin(θ) < -2?

• Between 0 and π/2

• Between π/6 and 5π/6

• Between π/2 and π

• Between 7π/6 and 11π/6

What is the reference angle for cos(θ) = √2/2?

• π/6

• π/2

• π/3

• π/4

In which quadrants is cos(θ) negative?

• First and fourth

• First and second

• Second and third

• Third and fourth

Which interval includes solutions for cos(θ) ≥ √2/2?

• π/2 to π

• π/4 to 3π/4

• 0 to π/4

• 0 to 3π/4

What is the solution set for f(x) = sin(x) ≤ 0?

• [0, π] ∪ [π, 2π]

• [0, 2π]

• [0, π/2] ∪ [3π/2, 2π]

• [π, 2π]

What is the significance of the purple line in the context of f(x) = sin(x) ≤ 0?

• It represents a horizontal displacement of 0

• It represents a vertical displacement of 0

• It represents a horizontal displacement of 1

• It represents a vertical displacement of 1