Whats the difference in their solutions and how you find it?

The video tutorial explains how to solve trigonometric equations using algebraic, graphical, and unit circle methods. It covers three examples: solving 2sin²θ - 1 = 0, 2sin(2θ) = -1, and sin(θ/2) = 1/2. Each example demonstrates different techniques, including inverse operations, substitution, and understanding the unit circle. The tutorial emphasizes finding solutions within specific intervals and for all possible values.

What methods are introduced for solving trigonometric equations?

• Algebraic, graphical, and unit circle

• Numerical and graphical

• Algebraic and numerical

• Graphical and statistical

What is the first step in solving the equation 2sin²(θ) - 1 = 0?

• Multiply both sides by 2

• Add 1 to both sides

• Subtract 1 from both sides

• Divide both sides by 2

What is the approximate value of ±√2/2?

• 0.5

• 0.7

• 1.0

• 1.4

Which angles correspond to the solutions of sin(θ) = ±√2/2 on the unit circle?

• π/3, 2π/3

• π/4, 3π/4, 5π/4, 7π/4

• π/2, 3π/2

• π/6, 5π/6

What substitution is used to solve 2sin(2θ) = -1?

• δ = 3θ

• β = 2θ

• γ = θ

• α = θ/2

What is the period of the function y = sin(2θ)?

• π/2

• 4π

• 2π

• π

What is the solution for sin(θ/2) = 1/2 within 0 to 2π?

• π/2 and 3π/2

• π/4 and 3π/4

• π/6 and 5π/6

• π/3 and 5π/3

How does dividing the angle by 2 affect the period of the sine function?

• It doubles the period

• It halves the period

• It quadruples the period

• It does not change the period

What is the general solution for sin(θ) = 1/2?

• θ = π/4 + 2πn

• θ = π/3 + 2πn

• θ = π/2 + 2πn

• θ = π/6 + 2πn

What is the importance of understanding the unit circle in solving trigonometric equations?

• It helps in finding the exact values of angles

• It is used to approximate solutions

• It only helps in graphical solutions

• It is not important