Evaluating Inverse Trigonometric Functions

TL;DR

Learn how to evaluate inverse sine, inverse cosine, and inverse tangent functions to find their exact values.

Transcript

now let's talk about evaluating inverse sine functions so let's say if we want to find the value of the inverse sine of one half what is that equal to what do you think the answer is now sine of what angle is equal to one-half if we could figure this out then we could find out what the value of arc sine one-half is now we know sine pi over six whic... Read More

Key Insights

• 🔺 Inverse trigonometric functions can be evaluated by finding the angle that corresponds to a given value.
• 🧡 The range of the function determines which quadrants the angle can be in.
• 🧡 It is important to consider the range of the inverse trigonometric function when choosing the appropriate angle.
• ❓ The values of certain inverse trigonometric functions can be rationalized to simplify the answers.

Questions & Answers

Q: What is the range of the arc sine function?

The arc sine function exists in quadrants 1 and 4 and has a range from -π/2 to π/2.

Q: How do we determine the value of arc sine one-half?

We look for angles in quadrants 1 and 4 where sine is equal to one-half. The answer is π/6.

Q: Can we use any angle in quadrants 1 and 2 as the value for arc cosine one-half?

No, the arc cosine function only exists in quadrants 1 and 2 and has a range from 0 to π. The value of arc cosine one-half is π/3.

Q: What is the range of the arc tangent function?

The arc tangent function exists in quadrants 1 and 4 and has a range from -π/2 to π/2.

Summary & Key Takeaways

• The inverse sine function, or arc sine, can only exist in quadrants 1 and 4 and has a range from -π/2 to π/2. The value of arc sine one-half is π/6.

• The inverse cosine function, or arc cosine, exists in quadrants 1 and 2 and has a range from 0 to π. The value of arc cosine one-half is π/3.

• The inverse tangent function, or arc tangent, exists in quadrants 1 and 4 and has a range from -π/2 to π/2. The value of arc tangent zero is 0.