Understanding Inverse Trigonometric Functions and Reference Triangles

The video tutorial explains how to evaluate the tangent of the inverse sine of a negative value. It begins by identifying the angle Theta and determining its quadrant based on the sign of the tangent. The tutorial then models the angle using a reference triangle in the fourth quadrant, applying the Pythagorean theorem to find the missing side. Finally, it calculates the tangent of Theta by taking the ratio of the opposite side to the adjacent side, simplifying the expression to -2/5.

What is the range of the inverse sine function?

• 0 to 2π

• -π/2 to π/2

• 0 to π

• -π to π

Tags

CCSS.HSF.TF.A.2

In which quadrants can angle Theta be located if its sine value is negative?

• Quadrant 3 and Quadrant 4

• Quadrant 1 and Quadrant 4

• Quadrant 2 and Quadrant 3

• Quadrant 1 and Quadrant 2

Tags

CCSS.HSF.TF.A.2

In which quadrant is angle Theta located if its tangent is negative?

• Quadrant 2

• Quadrant 1

• Quadrant 3

• Quadrant 4

Tags

CCSS.HSF.TF.A.2

What is the sine value of angle Theta in the reference triangle?

• -12/13

• 12/13

• -13/12

• 13/12

Tags

CCSS.HSG.SRT.C.6

Which side of the reference triangle is always positive?

• Hypotenuse

• None of the sides

• Adjacent side

• Opposite side

Tags

CCSS.HSF.TF.A.2

What is the length of the adjacent side in the reference triangle?

• -12

• 5

• -5

• 12

Tags

CCSS.8.G.B.8

Which theorem is used to find the length of the sides in a right triangle?

• Tangent rule

• Cosine rule

• Sine rule

• Pythagorean theorem

Tags

CCSS.8.G.B.7

If the hypotenuse is 13 and one leg is -12, what is the length of the other leg?

• -5

• 5

• 12

• -12

Tags

CCSS.HSG.SRT.C.6

How do you calculate the tangent of angle Theta using the reference triangle?

• Opposite side divided by adjacent side

• Hypotenuse divided by opposite side

• Adjacent side divided by hypotenuse

• Opposite side divided by hypotenuse

Tags

CCSS.HSF.TF.C.8

What is the simplified value of the tangent of angle Theta?

• -2/5

• 2/5

• -5/2

• 5/2

Tags

CCSS.HSF.TF.C.8