Trigonometric Functions and Equations

The video tutorial explains how to solve trigonometric equations using the unit circle and reference triangles. It covers two equations: 2sin(θ)=√3 and 2sin(θ)=-√2, demonstrating how to isolate sine, determine the quadrants where sine is positive or negative, and find solutions using both the unit circle and reference triangles. The tutorial emphasizes understanding the relationship between angles and their sine values, using reference triangles like 30-60-90 and 45-45-90 to find solutions without a calculator.

What is the first step in solving the equation 2sin(theta) = sqrt(3)?

• Divide both sides by 2

• Subtract 2 from both sides

• Multiply both sides by 2

• Add 2 to both sides

In which quadrants is the sine function positive?

• Third and fourth

• Second and fourth

• First and third

• First and second

What are the solutions for the equation 2sin(theta) = sqrt(3) using the unit circle?

• pi/4 and 3pi/4

• pi/2 and 3pi/2

• pi/3 and 2pi/3

• pi/6 and 5pi/6

Which reference triangle is used to solve 2sin(theta) = sqrt(3)?

• 30-60-90 triangle

• 60-60-60 triangle

• 90-90-90 triangle

• 45-45-90 triangle

What is the sine value of pi/3 radians?

• sqrt(2)/2

• 1/2

• 1

• sqrt(3)/2

In which quadrants is the sine function negative?

• First and second

• Second and third

• Third and fourth

• First and fourth

What are the solutions for the equation 2sin(theta) = -sqrt(2) using the unit circle?

• pi and 2pi

• pi/2 and 3pi/2

• pi/4 and 3pi/4

• 5pi/4 and 7pi/4

Which reference triangle is used to solve 2sin(theta) = -sqrt(2)?

• 30-60-90 triangle

• 45-45-90 triangle

• 60-60-60 triangle

• 90-90-90 triangle

What is the sine value of pi/4 radians?

• sqrt(3)/2

• 1/2

• sqrt(2)/2

• 1

What is the reference angle for a sine value of -sqrt(2)/2?

• 45 degrees

• 90 degrees

• 30 degrees

• 60 degrees