Understanding the Domain of Trigonometric Functions: Examining Denominators of Trig Ratios

This lesson explores the domain of the six trigonometric functions by examining the denominators of the trig ratios. It explains the unit circle's role in determining trig values, the reciprocal nature of certain functions, and how these functions extend beyond right triangles to circular functions. The domain of each function is discussed, particularly focusing on where they are undefined due to division by zero. The lesson emphasizes understanding the unit circle's coordinates and the importance of recognizing reciprocal pairs.

What is the reciprocal of the cosine function?

• Cosecant

• Tangent

• Secant

• Sine

How can all trigonometric functions be expressed?

• In terms of tangent and cotangent

• In terms of sine and cosine

• In terms of secant and cosecant

• In terms of angles and radians

What is the domain of sine and cosine functions?

• Only angles in a right triangle

• Only negative angles

• Only positive angles

• All real numbers

Why is the tangent function undefined at certain angles?

• Because the angle is negative

• Because both sine and cosine are zero

• Because cosine is zero

• Because sine is zero

At which angles is the secant function undefined?

• Multiples of 90 degrees

• Multiples of 45 degrees

• Multiples of 60 degrees

• Multiples of 180 degrees