Understanding the Domain of Secant and Cosecant Functions

The video tutorial explains how to use the unit circle to determine the domains of the secant and cosecant functions. It begins by defining cosine and sine in terms of the unit circle, where the radius is one. The secant and cosecant functions are introduced as reciprocals of cosine and sine, respectively. The tutorial then details how to exclude certain angles from the domains of these functions, based on where division by zero would occur. For the secant function, angles with terminal sides along the y-axis are excluded, while for the cosecant function, angles with terminal sides along the x-axis are excluded. The video concludes with a brief mention of similar considerations for tangent and cotangent functions.

What is the definition of cosine theta in terms of the unit circle?

• Y divided by R

• X divided by R

• R divided by X

• R divided by Y

Why must we exclude certain angles from the domain of secant and cosecant functions?

• Because they are always negative at those angles

• Because they are always one at those angles

• Because they are always zero at those angles

• Because they are undefined at those angles

Which axis must angles not lie on to be included in the domain of the secant function?

• X-axis

• Y-axis

• Z-axis

• W-axis

What is the pattern for angles excluded from the domain of the secant function?

• Multiples of 2pi

• Multiples of pi/2

• Multiples of pi

• Multiples of 3pi

Which coordinate must be zero for angles to be excluded from the domain of the cosecant function?

• X-coordinate

• Z-coordinate

• W-coordinate

• Y-coordinate

What is the pattern for angles excluded from the domain of the cosecant function?

• Multiples of 3pi

• Multiples of 2pi

• Multiples of pi

• Multiples of pi/2

What is the domain of the secant function in terms of theta?

• All reals where theta does not equal pi/2 + pi * k

• All reals where theta does not equal pi + pi * k

• All reals where theta does not equal 2pi + pi * k

• All reals where theta does not equal 3pi + pi * k

What is the domain of the cosecant function in terms of theta?

• All reals where theta does not equal 3pi + pi * k

• All reals where theta does not equal 2pi + pi * k

• All reals where theta does not equal pi + pi * k

• All reals where theta does not equal pi/2 + pi * k

Which trigonometric functions are mentioned as having similar domain considerations as secant and cosecant?

• Sine and Tangent

• Cosine and Cotangent

• Tangent and Cotangent

• Sine and Cosine

What is the significance of the unit circle in determining the domain of trigonometric functions?

• It helps define the domain

• It helps define the angles

• It helps define the radius

• It helps define the coordinates