Understanding Reference Angles and Tangent Function

The video tutorial explains how to find the two smallest positive angles that satisfy given conditions for a reference angle and a tangent function. It begins with an introduction to the problem, followed by a detailed explanation of reference angles and their properties. The tutorial then identifies the quadrants where the tangent is negative and sketches reference angles in these quadrants. Finally, it demonstrates how to calculate the smallest and second smallest positive angles that meet the conditions.

What is the reference angle given in the problem?

• 60 degrees

• 45 degrees

• 90 degrees

• 30 degrees

What is a reference angle?

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

• An angle that is always 90 degrees

• An angle that is always 180 degrees

• The positive acute angle formed by the x-axis and the terminal side

In which quadrants is the tangent of an angle negative?

• First and second quadrants

• First and third quadrants

• Second and fourth quadrants

• Third and fourth quadrants

What is the significance of the reference angle in determining the position of the terminal side?

• It is used to calculate the sine of the angle

• It helps in identifying the quadrant of the angle

• It is irrelevant to the position of the terminal side

• It determines the length of the terminal side

How do you find the smallest positive angle with a reference angle of 45 degrees in the second quadrant?

• Add 45 degrees to 90 degrees

• Subtract 45 degrees from 180 degrees

• Add 45 degrees to 180 degrees

• Subtract 45 degrees from 360 degrees

What is the measure of the smallest positive angle that satisfies the given conditions?

• 90 degrees

• 315 degrees

• 135 degrees

• 225 degrees

Which method can be used to find the smallest positive angle?

• Add the reference angle to 270 degrees

• Subtract the reference angle from 180 degrees

• Add the reference angle to 90 degrees

• Subtract the reference angle from 360 degrees

How can you find the second smallest positive angle with a reference angle of 45 degrees in the fourth quadrant?

• Subtract 45 degrees from 360 degrees

• Add 45 degrees to 270 degrees

• Subtract 45 degrees from 270 degrees

• Add 45 degrees to 360 degrees

What is the measure of the second smallest positive angle that satisfies the given conditions?

• 135 degrees

• 225 degrees

• 270 degrees

• 315 degrees

Which method can be used to find the second smallest positive angle?

• Add the reference angle to 90 degrees

• Add the reference angle to 180 degrees

• Subtract the reference angle from 180 degrees

• Subtract the reference angle from 360 degrees