Trigonometric Functions in Quadrants

The video tutorial covers three main problems in trigonometry. First, it explains how to find the cosine of an angle alpha in Quadrant II when the sine is given. The Pythagorean Identity is used to solve this. Next, it demonstrates how to find the cosine and sine of an angle theta when a point on its terminal side is known. Finally, it discusses how to find all angles with a sine of negative one-half, focusing on Quadrants III and IV and using reference angles.

What is the sine of alpha if alpha is a Quadrant II angle?

• -5/13

• 5/13

• 12/13

• -12/13

Which identity is used to find the cosine of an angle given its sine?

• Pythagorean Identity

• Sum of Angles Identity

• Double Angle Identity

• Half Angle Identity

What is the value of cosine squared alpha if sine alpha is 12/13?

• 0

• 1

• 144/169

• 25/169

In which quadrant is the cosine of an angle negative?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

What is the cosine of alpha if alpha is a Quadrant II angle with sine 12/13?

• 12/13

• -5/13

• -12/13

• 5/13

What is the point given on the terminal side of theta?

• (-3, 4)

• (3, 4)

• (-3, -4)

• (3, -4)

What is the formula for cosine of theta given a point on its terminal side?

• x^2 + y^2

• x^2 - y^2

• x / sqrt(x^2 + y^2)

• y / sqrt(x^2 + y^2)

What is the sine of theta if the point on the terminal side is (3, -4)?

• -3/5

• 3/5

• -4/5

• 4/5

What is the cosine of theta if the point on the terminal side is (3, -4)?

• -4/5

• 4/5

• -3/5

• 3/5

In which quadrants is the sine of an angle negative?

• Quadrants I and IV

• Quadrants I and II

• Quadrants II and III

• Quadrants III and IV