Trigonometric Functions and Quadrants

The video tutorial explains how to find the exact values of sine a and cosine a given that tangent a equals -5/7 and sine a is positive. It involves determining the quadrant of angle a, sketching the reference triangle, using the Pythagorean theorem to find the hypotenuse, and calculating the exact values of sine and cosine. The process includes rationalizing the denominator for the final values.

What is the first step in finding the exact values of sine and cosine given tangent and sine conditions?

• Determine the quadrant of the angle

• Calculate the hypotenuse

• Rationalize the denominator

• Sketch the reference triangle

In which quadrant is tangent negative and sine positive?

• First quadrant

• Second quadrant

• Third quadrant

• Fourth quadrant

What is the value of X in the reference triangle if tangent is -5/7?

• -7

• 7

• -5

• 5

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

• Sine theorem

• Cosine theorem

• Pythagorean theorem

• Tangent theorem

What is the exact value of R when calculated using the Pythagorean theorem?

• Square root of 49

• Square root of 74

• Square root of 25

• Square root of 100

How is sine a calculated from the reference triangle?

• Y divided by R

• X divided by R

• R divided by Y

• Y divided by X

What is the process called when you eliminate the square root from the denominator?

• Factoring

• Expanding

• Rationalizing

• Simplifying

What is the rationalized form of sine a?

• 5 square root of 74

• 5 square root of 74 divided by 74

• 5 divided by 74

• Square root of 74 divided by 5

What is the exact value of cosine a before rationalizing?

• Square root of 74 divided by -7

• -7 divided by square root of 74

• -7 square root of 74

• -7 divided by 74

What is the rationalized form of cosine a?

• -7 divided by 74

• -7 square root of 74 divided by 74

• -7 square root of 74

• Square root of 74 divided by -7