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

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

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

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

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

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

• Sine Rule

• Cosine Rule

• Pythagorean Theorem

• Tangent Rule

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

• 5

• Square root of 50

• 10

• 5 square root 2

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

What is the sine of angle A before rationalization?

• -7/5

• -7/10

• -7/5 square root 2

• -7 square root 2/10

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