Trigonometric Functions and Their Properties

The video tutorial explains how to find trigonometric function values given tangent theta equals negative five-thirds and sine theta is less than zero. It determines that theta is in the fourth quadrant, sketches a reference triangle, and uses the Pythagorean theorem to find the hypotenuse. The tutorial then calculates sine, cosine, and other trigonometric function values, and rationalizes the denominators of sine and cosine values.

In which quadrant is angle theta located if tangent theta is negative and sine theta is less than zero?

• First quadrant

• Second quadrant

• Third quadrant

• Fourth quadrant

What is the value of x if tangent theta is -5/3 and the terminal side is in the fourth quadrant?

• 3

• -5

• 5

• -3

How do you calculate the hypotenuse r using the Pythagorean theorem with x = 3 and y = -5?

• r = sqrt(9 - 25)

• r = sqrt(3 + 5)

• r = sqrt(9 + 25)

• r = sqrt(3 - 5)

What is the sine of theta if y = -5 and r = sqrt(34)?

• 3/sqrt(34)

• -3/sqrt(34)

• 5/sqrt(34)

• -5/sqrt(34)

What is the cosecant of theta if sine theta is -5/sqrt(34)?

• -sqrt(34)/5

• -5/sqrt(34)

• 5/sqrt(34)

• sqrt(34)/5

What is the cosine of theta if x = 3 and r = sqrt(34)?

• -3/sqrt(34)

• 3/sqrt(34)

• -5/sqrt(34)

• 5/sqrt(34)

What is the secant of theta if cosine theta is 3/sqrt(34)?

• -3/sqrt(34)

• 3/sqrt(34)

• -sqrt(34)/3

• sqrt(34)/3

What is the cotangent of theta if x = 3 and y = -5?

• 5/3

• -5/3

• 3/5

• -3/5

How do you rationalize the denominator of -5/sqrt(34)?

• Multiply by 5/5

• Multiply by 34/34

• Multiply by -5/-5

• Multiply by sqrt(34)/sqrt(34)

What is the rationalized form of the cosine function value 3/sqrt(34)?

• 5sqrt(34)/34

• -3sqrt(34)/34

• 3sqrt(34)/34

• -5sqrt(34)/34