Trigonometric Functions and Their Properties

This video tutorial explores the domain of the six trigonometric functions by examining the denominators of the trig ratios. It begins with an introduction to the unit circle and the basic trigonometric ratios, including sine, cosine, and tangent. The video then discusses the reciprocal relationships among trigonometric functions, such as secant, cosecant, and cotangent. It further explains how trigonometric functions can be viewed as circular functions due to their connection to the unit circle. Finally, the tutorial details the domain of each trigonometric function, highlighting where they are undefined due to division by zero.

Why can't a calculator find the tangent of 90 degrees?

• Because the tangent function is undefined at 90 degrees

• Because calculators do not support trigonometric functions

• Because 90 degrees is not a valid angle

• Because 90 degrees is outside the range of the tangent function

What is the reciprocal of the cosine function?

• Tangent

• Secant

• Cosecant

• Sine

Which coordinate on the unit circle represents the sine of an angle?

• X-coordinate

• Origin

• Y-coordinate

• Z-coordinate

What is a helpful way to remember reciprocal pairs of trigonometric functions?

• Each pair has one 'co' prefix

• They all start with the letter 'S'

• They are all even functions

• They are all odd functions

How can all trigonometric functions be rewritten?

• In terms of sine and cosine

• In terms of secant and cosecant

• In terms of angles and radians

• In terms of tangent and cotangent

What are trigonometric functions referred to as due to their connection to the unit circle?

• Circular functions

• Exponential functions

• Quadratic functions

• Linear functions

What is the domain of sine and cosine functions?

• Only positive angles

• Only negative angles

• All real numbers

• Only angles in a right triangle

Why is the tangent function undefined at certain angles?

• Because the angle is not a real number

• Because both sine and cosine are zero at those angles

• Because cosine is zero at those angles

• Because sine is zero at those angles

At which angles is the cosine function zero?

• 45 and 135 degrees

• 0 and 180 degrees

• 60 and 120 degrees

• 90 and 270 degrees

Where are the last two trigonometric functions undefined?

• Where secant is zero

• Where cosine is zero

• Where tangent is zero

• Where sine is zero