Trigonometric Functions and Properties

The video tutorial covers various aspects of trigonometry, including the unit circle, trigonometric identities, periodicity, and symmetry properties. It explains how to calculate secant and cotangent using the unit circle and reference angles. The tutorial also demonstrates the use of graphing calculators for approximations and applies trigonometry to solve real-world problems.

On the unit circle, at which angles are sine and cosine equal?

• π/6 and 7π/6

• π/2 and 3π/2

• π/4 and 5π/4

• π/3 and 4π/3

What is the period of the tangent function?

• π/2

• 4π

• 2π

• π

How do you calculate the secant of an angle using the unit circle?

• 1 over the y-coordinate

• 1 over the x-coordinate

• The y-coordinate

• The x-coordinate

What is the reference angle for 7π/6?

• π/2

• π/6

• π/3

• π/4

In which quadrant are both sine and cosine positive?

• Quadrant III

• Quadrant I

• Quadrant II

• Quadrant IV

What is the symmetry property of sine regarding negative angles?

• Sine of negative angle is cosine of angle

• Sine of negative angle is tangent of angle

• Sine of negative angle is negative sine of angle

• Sine of negative angle is positive sine of angle

What is the reciprocal of cosine known as?

• Cosecant

• Sine

• Tangent

• Secant

How do you determine if a trigonometric function is even?

• If f(-x) = -f(x)

• If f(-x) = f(x)

• If f(-x) = 0

• If f(-x) = 1

What is the period of a cosine function with a coefficient of 1/500 in front of x?

• 2π

• 1000π

• 500π

• π

Using a graphing calculator, what mode should you be in to evaluate trigonometric functions with π?

• Decimal

• Gradians

• Radians

• Degrees