Trigonometric Functions and Their Properties

The video tutorial explains how to evaluate the trigonometric expression sin of inverse tangent of -7. It begins by identifying the angle using inverse tangent and sets up a reference triangle in quadrant four due to the negative tangent value. The Pythagorean theorem is applied to find the hypotenuse, and the sine of the angle is calculated and rationalized to obtain the final expression.

What is the initial trigonometric expression we want to evaluate?

• Tangent of inverse sine of -7

• Sine of inverse cosine of -7

• Sine of inverse tangent of -7

• Cosine of inverse tangent of -7

Tags

CCSS.HSF.TF.B.7

What does the inverse tangent of -7 return?

• An angle with a tangent value of 1/-7

• An angle with a tangent value of -7/1

• An angle with a cosine value of -7

• An angle with a sine value of -7

Tags

CCSS.HSF.TF.A.2

In which quadrants can the angle A be located based on the range of inverse tangent?

• Quadrant II or III

• Quadrant I or II

• Quadrant III or IV

• Quadrant I or IV

Tags

CCSS.HSF.TF.A.2

Why must the reference triangle be in quadrant four?

• Because the tangent value is positive

• Because the tangent value is negative

• Because the sine value is positive

• Because the cosine value is negative

Tags

CCSS.HSF.TF.A.2

What are the lengths of the opposite and adjacent sides in the reference triangle?

• Opposite: -7, Adjacent: 1

• Opposite: 7, Adjacent: -1

• Opposite: 1, Adjacent: -7

• Opposite: -1, Adjacent: 7

Tags

CCSS.8.G.B.8

Which theorem is used to find the hypotenuse of the reference triangle?

• Sine Rule

• Cosine Rule

• Pythagorean Theorem

• Tangent Rule

Tags

CCSS.8.G.B.7

What is the length of the hypotenuse in the reference triangle?

• 5

• Square root of 50

• 10

• 5 square root 2

Tags

CCSS.HSG.SRT.C.6

How is the sine of angle A calculated?

• Ratio of hypotenuse to opposite side

• Ratio of hypotenuse to adjacent side

• Ratio of opposite side to hypotenuse

• Ratio of adjacent side to hypotenuse

Tags

CCSS.HSF.TF.C.8

What is the sine of angle A before rationalization?

• -7/5

• -7/10

• -7/5 square root 2

• -7 square root 2/10

Tags

CCSS.HSF.TF.C.8

What is the final rationalized expression for the sine of angle A?

• -7 square root 2/5

• -7/10

• -7 square root 2/10

• -7/5 square root 2

Tags

CCSS.HSF.TF.C.8