Inverse Trig Functions

Front

What are inverse trigonometric functions?

Back

Inverse trigonometric functions are functions that reverse the action of the standard trigonometric functions. They take a ratio (like sine, cosine, or tangent) and return an angle.

Front

What is the range of the arcsine function, sin^-1(x)?

Back

The range of the arcsine function is [-π/2, π/2].

Front

What is the range of the arccosine function, cos^-1(x)?

Back

The range of the arccosine function is [0, π].

Front

What is the range of the arctangent function, tan^-1(x)?

Back

The range of the arctangent function is (-π/2, π/2).

Front

What is the relationship between the sine and cosecant functions?

Back

The cosecant function is the reciprocal of the sine function: csc(x) = 1/sin(x).

Front

How do you evaluate csc^-1(x)?

Back

To evaluate csc^-1(x), find the angle whose cosecant is x, ensuring the angle is in the range of [-π/2, 0) ∪ (0, π/2].

Front

What is the value of csc^-1(-√2)?

Back

The value of csc^-1(-√2) is -π/4.

Front

How do you evaluate cos^-1(x)?

Back

To evaluate cos^-1(x), find the angle whose cosine is x, ensuring the angle is in the range of [0, π].

Front

What is the value of cos^-1(√3/2)?

Back

The value of cos^-1(√3/2) is π/6.

Front

What is the domain of the arcsine function, sin^-1(x)?

Back

The domain of the arcsine function is [-1, 1].