An Introduction to Inverse Trigonometric Functions (6.7.1)

Question 1

• Review: In order for a function, f(x), to have an inverse , f^–1(x), it must be a one-to-one function (ie: it must pass the horizontal line test).

Answer 1

• Review: In order for a function, f(x), to have an inverse , f^–1(x), it must be a one-to-one function (ie: it must pass the horizontal line test).

Question 2

• The basic trigonometric functions have inverses if their domains are restricted. These inverse functions are known as the inverse trigonometric functions:
• The inverse sine function is written y = sin^–1x. (Think of sin^–1x as “the angle whose sine is x.”)
The domain for y = sin^–1x is -1≤x≤1 and the range is (-π/2)≤y≤(π/2).
• The inverse cosine function is written y = cos–1x. (Think of cos^–1x as “the angle whose cosine is x.”)
The domain for y = cos^–1x is -1≤x≤1 and the range is 0≤y≤π.
• The inverse tangent function is written y = tan–1x. (Think of tan–1x as “the angle whose tangent is x.”)
The domain for y = tan–1x is any real number and the range is (-π/2)≤y≤(π/2).

Answer 2

• The basic trigonometric functions have inverses if their domains are restricted. These inverse functions are known as the inverse trigonometric functions:
• The inverse sine function is written y = sin^–1x. (Think of sin^–1x as “the angle whose sine is x.”)
The domain for y = sin^–1x is -1≤x≤1 and the range is (-π/2)≤y≤(π/2).
• The inverse cosine function is written y = cos–1x. (Think of cos^–1x as “the angle whose cosine is x.”)
The domain for y = cos^–1x is -1≤x≤1 and the range is 0≤y≤π.
• The inverse tangent function is written y = tan–1x. (Think of tan–1x as “the angle whose tangent is x.”)
The domain for y = tan–1x is any real number and the range is (-π/2)≤y≤(π/2).