Evaluating Inverse Trig Functions

Front

What is the definition of arcsin?

Back

Arcsin, or inverse sine, is a function that returns the angle whose sine is a given number. It is defined for values in the range [-1, 1] and returns angles in the range [-90°, 90°].

Tags

CCSS.HSF-BF.B.4D

Front

What is the value of arcsin 1?

Back

90°

Tags

CCSS.HSF.TF.B.7

Front

What is the value of arcsin \( \frac{\sqrt{2}}{2} \)?

Back

45°

Tags

CCSS.HSF.TF.B.7

Front

What is the definition of arccos?

Back

Arccos, or inverse cosine, is a function that returns the angle whose cosine is a given number. It is defined for values in the range [-1, 1] and returns angles in the range [0°, 180°].

Tags

CCSS.HSF.TF.B.7

Front

What is the value of arccos 1?

Back

0°

Tags

CCSS.HSF.TF.B.7

Front

What is the value of arccos \( -\frac{\sqrt{3}}{2} \)?

Back

150°

Tags

CCSS.HSF.TF.B.7

Front

Evaluate: sin[arcsin(\frac{1}{2})]

Back

\frac{1}{2}.

Tags

CCSS.HSF.TF.B.7

Front

What is the range of the arcsin function?

Back

The range of the arcsin function is [-90°, 90°].

Tags

CCSS.HSF-BF.B.4D

Front

What is the range of the arccos function?

Back

The range of the arccos function is [0°, 180°].

Tags

CCSS.HSF-BF.B.4D

Front

If sin(θ) = \frac{1}{2}, what is θ?

Back

θ = 30° or θ = 150°.

Tags

CCSS.HSF.TF.B.7