Trigonometric Functions and Their Properties

This video tutorial explores trigonometric values for angles greater than 90 degrees using reference triangles and the unit circle. It explains the concept of supplementary angles, the unit circle's properties, and how to extend sine and cosine to angles beyond 90 degrees. The tutorial also covers the reflection of triangles over axes and the calculation of trigonometric values in different quadrants.

Why is it important to use reference triangles for angles greater than 90 degrees?

• To simplify calculations

• To extend trigonometric values beyond right triangles

• To avoid using the unit circle

• To measure angles in degrees only

What is the radius of the unit circle?

• 3.14

• 0.5

• 1

• 2

How is the sine of an angle defined in the unit circle?

• As the length of the hypotenuse

• As the x-coordinate of the point

• As the y-coordinate of the point

• As the angle in radians

What happens to the cosine value when a triangle is reflected over the y-axis?

• It becomes negative

• It remains unchanged

• It becomes zero

• It becomes positive

In which quadrant are both sine and cosine negative?

• First quadrant

• Second quadrant

• Third quadrant

• Fourth quadrant

What is the relationship between alpha and theta in the fourth quadrant?

• Alpha equals 180 degrees plus theta

• Alpha equals 360 degrees minus theta

• Alpha equals 180 degrees minus theta

• Alpha equals theta

How do you calculate secant of an angle?

• Sine divided by cosine

• 1 divided by cosine

• Cosine divided by sine

• 1 divided by sine

What is the approximate value of 2 pi in degrees?

• 90 degrees

• 360 degrees

• 270 degrees

• 180 degrees

Which trigonometric function is the reciprocal of tangent?

• Sine

• Cotangent

• Cosecant

• Cosine

What is the significance of the unit circle in trigonometry?

• It is used only for angles less than 90 degrees

• It provides a way to define trigonometric functions for all angles

• It simplifies the calculation of angles in radians

• It helps in measuring angles in degrees