Inverse Trig Ratios

Front

What is the definition of inverse trigonometric functions?

Back

Inverse trigonometric functions are functions that determine the angle whose trigonometric ratio is a given number. They include sin^–1, cos^–1, and tan^–1.

Front

What is sin^–1(x)?

Back

sin^–1(x) is the angle whose sine is x. It is defined for x in the range [-1, 1].

Front

What is cos^–1(x)?

Back

cos^–1(x) is the angle whose cosine is x. It is defined for x in the range [-1, 1].

Front

What is tan^–1(x)?

Back

tan^–1(x) is the angle whose tangent is x. It is defined for all real numbers.

Front

What is the range of sin^–1(x)?

Back

The range of sin^–1(x) is [-90º, 90º] or [-π/2, π/2] in radians.

Front

What is the range of cos^–1(x)?

Back

The range of cos^–1(x) is [0º, 180º] or [0, π] in radians.

Front

What is the range of tan^–1(x)?

Back

The range of tan^–1(x) is (-90º, 90º) or (-π/2, π/2) in radians.

Front

If sin(x) = 1/2, what is x?

Back

x = 30º or x = 150º.

Front

If cos(x) = 1/2, what is x?

Back

x = 60º or x = 300º.

Front

If tan(x) = 1, what is x?

Back

x = 45º or x = 225º.