Unit Circle and Trigonometric Functions

The video tutorial explains the trigonometric functions of real numbers, starting with the formula for the length of a circular arc. It introduces the unit circle, where the radius is one, and demonstrates how the arc length equals the radian measure of the central angle. The tutorial then uses coordinates on the unit circle to define the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. An example is provided to illustrate how to calculate these functions using a point on the unit circle.

What is the formula for the length of a circular arc?

• s = theta / r

• s = r / theta

• s = r * theta

• s = r + theta

If a circle has a radius of 5 inches and an angle of pi/3 radians, what is the arc length?

• 5.2 inches

• 5 inches

• 6 inches

• 5.5 inches

What is a unit circle?

• A circle with radius 1

• A circle with radius 3

• A circle with radius 2

• A circle with radius 0.5

In a unit circle, what is the relationship between the arc length and the angle in radians?

• Arc length equals the angle

• Arc length is double the angle

• Arc length is the square of the angle

• Arc length is half the angle

What is the circumference of a unit circle?

• pi/2

• 4 pi

• pi

• 2 pi

How is the sine function defined using the unit circle?

• Sine of t equals x-coordinate

• Sine of t equals y-coordinate

• Sine of t equals y/x

• Sine of t equals x/y

What is the cosine of t if the point on the unit circle is (sqrt(3)/2, 1/2)?

• sqrt(3)/3

• 2/sqrt(3)

• sqrt(3)/2

• 1/2

What is the tangent of t if the point on the unit circle is (sqrt(3)/2, 1/2)?

• 1/sqrt(3)

• 3/sqrt(3)

• sqrt(3)/3

• sqrt(3)

What is the secant of t if the point on the unit circle is (sqrt(3)/2, 1/2)?

• 3/sqrt(3)

• 2/sqrt(3)

• sqrt(3)/2

• 2

What is the cotangent of t if the point on the unit circle is (sqrt(3)/2, 1/2)?

• sqrt(3)

• 1/sqrt(3)

• sqrt(3)/2

• 2/sqrt(3)