Trigonometric Functions and Ratios

The video tutorial explains how to determine primary trigonometric ratios for angles greater than 90 degrees using a coordinate plane. It introduces the concept of defining sine, cosine, and tangent in all four quadrants, considering the signs of x, y, and r. The tutorial provides examples in each quadrant, demonstrating how to calculate these ratios using specific points and the Pythagorean theorem. The video emphasizes understanding the reference angle and its role in determining the trigonometric ratios.

What is the main focus of this video tutorial?

• Learning about the coordinate plane

• Exploring the history of trigonometry

• Determining primary trigonometric ratios for angles greater than 90 degrees

• Understanding trigonometric ratios for angles less than 90 degrees

In which quadrant is the rotation angle initially created?

• First quadrant

• Second quadrant

• Third quadrant

• Fourth quadrant

What are the three sides of a right triangle labeled as?

• Opposite, adjacent, and hypotenuse

• X, Y, and Z

• Base, height, and hypotenuse

• Radius, diameter, and circumference

What do X and Y represent on the coordinate plane?

• X is the adjacent, Y is the hypotenuse

• X is the hypotenuse, Y is the opposite

• X is the x-direction, Y is the y-direction

• X is the radius, Y is the diameter

How is sine defined in terms of Y, X, and R?

• R over Y

• X over R

• Y over X

• Y over R

What is the sign of X in the second quadrant?

• Negative

• Positive

• Zero

• Undefined

In the first quadrant, what are the trigonometric ratios for a point (3, 4)?

• Sine: 4/5, Cosine: 3/5, Tangent: 4/3

• Sine: 3/5, Cosine: 4/5, Tangent: 4/3

• Sine: 4/5, Cosine: 3/5, Tangent: 3/4

• Sine: 3/5, Cosine: 4/5, Tangent: 3/4

In the second quadrant, what is the sign of the cosine function?

• Negative

• Undefined

• Zero

• Positive

For a point (-3, -4) in the third quadrant, what is the tangent ratio?

• 4/3

• -3/4

• -4/3

• 3/4

In the fourth quadrant, which trigonometric function is positive?

• Tangent

• Cosine

• None

• Sine