Math 1113: Module 8-11 Review

This set of flashcards covers key concepts from inverse trigonometric functions, equation solving, trigonometric identities, and angle evaluations relevant to Math 1113.

What is the domain of the arcsine function, arcsin x?

[-1, 1]

What is the range of the arcsine function, arcsin x?

[π/2, -π/2]

What is the domain of the arccosine function, arccos x?

[-1, 1]

What is the range of the arccosine function, arccos x?

[0, π]

How do you evaluate tan(π/6)?

tan(π/6) = √3/3.

What is the output of Arctan(1)?

π/4.

What is the general solution for sinx = 1/2?

x = π/6 + 2kπ or x = 5π/6 + 2kπ, where k is any integer.

Solve for x: 2cos²x - 1 = 0

x = π/4 + kπ or x = -π/4 + kπ, where k is any integer.

What identity is represented by csc²x(1 - sec²x)?

sec²x.

What is the sum formula for tan(75°) using angle addition?

tan(75°) = tan(45° + 30°) = (tan 45 + tan 30) / (1 - tan 45 * tan 30).