Understanding Trigonometric Expressions

The video tutorial explains how to evaluate the tangent of the inverse sine of -12/13. It begins by identifying the angle theta, which has a sine value of -12/13, and determines that theta is in the fourth quadrant. A reference triangle is used to model the angle, and the Pythagorean theorem is applied to find the missing side length. Finally, the tangent of angle theta is calculated as the ratio of the opposite side to the adjacent side, resulting in -12/5.

What is the angle theta when evaluating the inverse sine of -12/13?

• An angle with a sine value of -12/13

• An angle with a tangent value of -12/13

• An angle with a sine value of 12/13

• An angle with a cosine value of -12/13

In which quadrant does angle theta lie if its tangent is negative?

• Quadrant 1

• Quadrant 2

• Quadrant 3

• Quadrant 4

What is the purpose of modeling angle theta with a reference triangle?

• To find the sine of theta

• To find the tangent of theta

• To find the cosine of theta

• To find the secant of theta

What are the lengths of the sides of the reference triangle used for angle theta?

• 7, 24, 25

• 3, 4, 5

• 5, 12, 13

• 6, 8, 10

How do you determine the length of the missing side in the reference triangle?

• Using the tangent rule

• Using the sine rule

• Using the cosine rule

• Using the Pythagorean theorem

What is the value of x in the reference triangle if x^2 + 144 = 169?

• 6

• 3

• 4

• 5

Why is the x-coordinate positive in the fourth quadrant?

• Because the y-coordinate is negative

• Because the x-coordinate is always positive

• Because the angle is in the fourth quadrant

• Because the hypotenuse is positive

What is the tangent of angle theta in the reference triangle?

• 12/5

• 5/12

• -12/5

• -5/12

What does the expression -12/5 represent in the context of this problem?

• The secant of theta

• The sine of theta

• The cosine of theta

• The tangent of theta

What is the final simplified expression for the tangent of the inverse sine of -12/13?

• -5/12

• 12/5

• -12/5

• 5/12