Inverse Trigonometric Functions Concepts

This video tutorial covers evaluating trigonometric expressions involving both trigonometric and inverse trigonometric functions. It provides three examples: inverse sine of sine PI/3, inverse sine of cosine -3PI/4, and inverse tangent of sine -PI/6. Each example is explained using reference triangles and the appropriate intervals for inverse functions. The video emphasizes the importance of understanding the range restrictions of inverse functions and demonstrates how to use a calculator for non-standard angles.

What is the main focus of the video tutorial?

• Understanding calculus concepts

• Solving quadratic equations

• Evaluating trigonometric expressions involving both trig and inverse trig functions

• Evaluating algebraic expressions

In the first example, what is the sine of pi/3?

• 1

• Square root 2/2

• Square root 3/2

• 1/2

What is the range of the inverse sine function?

• 0 to pi

• -pi/2 to pi/2

• -pi to pi

• 0 to 2pi

In the second example, what is the cosine of -3pi/4?

• -1/2

• 1/square root 2

• -1/square root 2

• 1/2

Why is it necessary to consider the range of the inverse sine function?

• To ensure the angle is positive

• To restrict the output to a specific interval

• To simplify calculations

• To avoid using a calculator

In the third example, what is the sine of -pi/6?

• 1/2

• -1/2

• -square root 3/2

• square root 3/2

What is the range of the inverse tangent function?

• 0 to pi

• -pi/2 to pi/2

• -pi to pi

• 0 to 2pi

Why is a calculator used in the third example?

• To find the exact value of the hypotenuse

• To check the accuracy of the reference triangle

• To convert radians to degrees

• To approximate the angle in degrees and radians

What is the approximate angle in degrees for the inverse tangent of -1/2?

• -45 degrees

• -30 degrees

• -26.6 degrees

• -60 degrees

What is the approximate angle in radians for the inverse tangent of -1/2?

• -0.5 radians

• -0.46 radians

• -0.6 radians

• -0.3 radians