Trigonometric Functions in Quadrant Three

The video tutorial explains how to determine trigonometric function values for an angle in the third quadrant, given that sine theta equals -5/7. It involves modeling the angle, sketching a reference triangle, and using the Pythagorean theorem to find the missing side. The tutorial then calculates cosine, secant, tangent, and cotangent values, including rationalizing denominators where necessary.

What is the sine value of angle theta in the third quadrant?

• -7/5

• 5/7

• -5/7

• 7/5

In which quadrant is the angle theta located?

• First

• Second

• Third

• Fourth

What is the reference angle for theta?

• The angle between the initial side and the y-axis

• The angle between the initial side and the x-axis

• The angle between the terminal side and the y-axis

• The angle between the terminal side and the x-axis

What is the length of the adjacent side in the reference triangle if the opposite side is -5 and the hypotenuse is 7?

• -√24

• √24

• -2√6

• 2√6

What is the cosine of theta in the third quadrant?

• -2√6/7

• -7/2√6

• 2√6/7

• 7/2√6

How do you rationalize the denominator of -7/(2√6)?

• Multiply by 6/6

• Multiply by 7/7

• Multiply by 2/2

• Multiply by √6/√6

What is the cosecant of theta if sine theta is -5/7?

• 7/5

• -7/5

• 5/7

• -5/7

What is the tangent of theta in the third quadrant?

• -2√6/5

• 2√6/5

• -5/(2√6)

• 5/(2√6)

What is the cotangent of theta if tangent theta is 5/(2√6)?

• 2√6/5

• -5/(2√6)

• -2√6/5

• 5/(2√6)

What is the reciprocal of the tangent function?

• Cotangent

• Secant

• Cosine

• Sine