Domain and Range of Trigonometric Functions

The video tutorial explains the concepts of domain and range for trigonometric functions. It covers the domain and range of sine, cosine, and tangent functions, highlighting that sine and cosine are defined for all real numbers with a range between -1 and 1. The tangent function is defined for all real numbers except odd multiples of π/2, with a range of all real numbers. The video also discusses how adding or multiplying constants affects these functions, and it extends the discussion to cotangent, cosecant, and secant functions, explaining their domains and ranges.

What is the domain of the sine and cosine functions?

• All real numbers

• All integers

• All negative numbers

• All positive numbers

What is the range of the sine and cosine functions?

• Open interval (-1, 1)

• All real numbers

• Closed interval [-1, 1]

• Open interval (0, 1)

For which values is the tangent function not defined?

• Even multiples of pi

• Odd multiples of pi/2

• All real numbers

• All integers

What is the range of the tangent function?

• Closed interval [-1, 1]

• All real numbers

• Open interval (0, 1)

• Open interval (-1, 1)

How does multiplying the sine and cosine functions by a constant affect their range?

• The range becomes [a, a]

• The range remains [-1, 1]

• The range becomes [0, a]

• The range becomes [-a, a]

For which values is the cotangent function not defined?

• Odd multiples of pi/2

• All real numbers

• Integral multiples of pi

• All integers

What is the range of the cosecant function when multiplied by a constant?

• All real numbers

• Values less than or equal to -a and greater than or equal to a

• Open interval (0, 1)

• Closed interval [-1, 1]