Trigonometric Functions and Unit Circle

This video tutorial covers solving trigonometric equations, focusing on sine and cosine waves. It explains the properties of these waves and how they relate to the unit circle. The tutorial demonstrates solving equations graphically and using calculators, with examples in both degrees and radians. It also includes advanced problem-solving techniques for trigonometric equations.

What does the sine wave represent in the unit circle?

• The angle

• The x-values

• The radius

• The y-values

At what point does the cosine wave start on the unit circle?

• At 1

• At 0.5

• At -1

• At 0

What does the equation 'cosine of theta equals 0.4' signify?

• Angles that produce a radius of 0.4

• Angles that produce a tangent of 0.4

• Angles that produce an x-value of 0.4

• Angles that produce a y-value of 0.4

How many solutions exist for the equation 'cosine of theta equals 0.4' between -360 and 360 degrees?

• 4

• 5

• 3

• 2

What is the first step in solving 'cosine of theta equals 0.4' using a calculator?

• Find the cosine of 0.4

• Find the tangent of 0.4

• Find the inverse cosine of 0.4

• Find the sine of 0.4

What mode should your calculator be in when solving trigonometric equations in degrees?

• Graphing mode

• Scientific mode

• Degree mode

• Radian mode

What angle produces a y-value of 0.5 in the unit circle?

• 30 degrees

• 90 degrees

• 60 degrees

• 45 degrees

How many solutions exist for 'sine of x equals 0.5' between -360 and 360 degrees?

• 2

• 3

• 4

• 5

What is the radian measure for an angle that produces a y-value of 0.5?

• π/3

• π/6

• π/4

• π/2

What angles produce a tangent value of √3?

• π/2 and 3π/2

• π/3 and 4π/3

• π/6 and 5π/6

• π/4 and 7π/4