Trigonometric Functions in the Third Quadrant

The video tutorial explains how to determine the trigonometric function values for an angle theta in the third quadrant, given that sine theta equals negative 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, cosecant, tangent, and cotangent values, including rationalizing denominators where necessary. The process emphasizes understanding the reference triangle and the signs of trigonometric functions in different quadrants.

In which quadrant is theta located if sine theta is negative?

• First quadrant

• Second quadrant

• Fourth quadrant

• Third quadrant

What is the reference angle for theta in the third quadrant?

• 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 x-axis

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

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

• 2√6

• -2√6

• √24

• -√24

How do you calculate cosine theta using the reference triangle?

• Hypotenuse divided by adjacent side

• Opposite side divided by hypotenuse

• Adjacent side divided by hypotenuse

• Hypotenuse divided by opposite side

What is the rationalized form of secant theta if it is initially -7/(2√6)?

• 7/12

• -7/12

• 7√6/12

• -7√6/12

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

• -5/7

• -7/5

• 7/5

• 5/7

How is tangent theta calculated using the reference triangle?

• Hypotenuse divided by adjacent side

• Hypotenuse divided by opposite side

• Adjacent side divided by opposite side

• Opposite side divided by adjacent side

What is the rationalized form of tangent theta if it is initially 5/(2√6)?

• -5/12

• 5√6/12

• -5√6/12

• 5/12

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

• 2√6/5

• -2√6/5

• 5/2√6

• -5/2√6

What is the importance of modeling the angle and reference triangle in trigonometry?

• To determine the angle's position

• To find additional trigonometric values

• To calculate the hypotenuse

• To identify the quadrant