Trigonometric Functions and Their Properties

The video tutorial covers the evaluation of inverse trigonometric functions, focusing on inverse sine and cosine. It explains how these functions return angles and how to use these angles to find sine, cosine, and tangent values. The tutorial includes examples with reference triangles and the Pythagorean theorem to determine side lengths and function values.

What does an inverse trigonometric function return?

• A side length

• An angle

• A ratio

• A quadrant

If the inverse sine of a value is taken, what is the result when the sine of that angle is calculated?

• The original value

• The square of the original value

• Half the original value

• Twice the original value

In which quadrant is the reference triangle located when the sine function value is positive?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the cosine function value of an angle if the inverse cosine of -2/7 is given?

• 7/2

• -2/7

• 2/7

• -7/2

What is the range of angles for the inverse cosine function?

• -π to π

• 0 to 2π

• -π/2 to π/2

• 0 to π

In the complex example, what is the length of the opposite side if the adjacent side is 2 and the hypotenuse is 3?

• 2

• √5

• 1

• 3

How do you calculate the tangent of an angle in a right triangle?

• Opposite side divided by adjacent side

• Hypotenuse divided by opposite side

• Opposite side divided by hypotenuse

• Adjacent side divided by hypotenuse

What theorem is used to find the missing side of a triangle in the complex example?

• Sine Rule

• Cosine Rule

• Pythagorean Theorem

• Tangent Rule

What is the tangent of the angle θ if the opposite side is √5 and the adjacent side is 2?

• 2/5

• √5/2

• 5/2

• 2/√5

What will be covered in the next video?

• More problems like the ones discussed

• Introduction to calculus

• Advanced algebraic equations

• Basic geometry concepts