Tangent Function Concepts and Properties

The video tutorial explains the tangent function, focusing on its domain, range, period, symmetry, x-intercepts, vertical asymptotes, and key points. The domain excludes values where cosine is zero, while the range includes all real numbers. The period is pi, and the function is odd, showing symmetry at the origin. X-intercepts occur at multiples of pi, and vertical asymptotes are at pi/2 plus multiples of pi. Key points are identified where sine and cosine have equal magnitudes.

What is the domain of the tangent function?

• All x values except where sine is zero

• All x values except where tangent is zero

• All real numbers

• All x values except where cosine is zero

What is the range of the tangent function?

• All numbers between -1 and 1

• All negative numbers

• All positive numbers

• All real numbers

What is the period of the tangent function?

• 2π

• π

• 4π

• π/2

What type of symmetry does the tangent function exhibit?

• Symmetry about the y-axis

• Symmetry about the x-axis

• Symmetry about the origin

• No symmetry

Where do the x-intercepts of the tangent function occur?

• At multiples of π/4

• At multiples of π

• At multiples of π/2

• At multiples of 2π

Where do the vertical asymptotes of the tangent function occur?

• At x = π plus any multiple of π

• At x = 0 plus any multiple of π

• At x = π/2 plus any multiple of π

• At x = π/4 plus any multiple of π

What is a key point on the tangent graph when x equals π/4?

• (π/4, -1)

• (π/4, 1)

• (π/4, 0)

• (π/4, π)

What happens to the tangent function at x = -π/4?

• It equals π

• It equals -1

• It equals 1

• It equals 0

What is the value of tangent when sine and cosine have the same magnitude?

• Undefined

• 0

• 1

• -1

What is the value of tangent when sine is negative and cosine is positive?

• Undefined

• 1

• 0

• -1