Understanding Reference Angles and Terminal Points

The video tutorial explains how to find the reference angle and the smallest possible positive angle for a point on the terminal side of an angle. It begins by plotting the point and using the tangent function to find the angle. The tutorial demonstrates using a calculator to find the inverse tangent and explains the significance of the reference angle. It also discusses the relationship between angles in different quadrants and concludes by calculating the smallest positive angle in radians.

What is the initial step in solving for the reference angle and smallest positive angle for a point on the terminal side?

• Find the midpoint of the line

• Determine the cosine of the angle

• Plot the point on the coordinate plane

• Calculate the sine of the angle

What is the formula for tangent in terms of coordinates on the plane?

• y minus x

• x divided by y

• y divided by x

• x plus y

How do you solve for angle 'a' using the tangent function?

• Use the inverse cosine function

• Use the inverse sine function

• Use the inverse tangent function

• Use the inverse cotangent function

Why is it important to ensure the calculator is in radian mode?

• To get the angle in degrees

• To ensure the angle is in radians

• To convert the angle to a fraction

• To simplify the calculation

What is the reference angle for the angle in the first quadrant?

• 1.2925 radians

• 2.2925 radians

• 4.2925 radians

• 3.2925 radians

How is the reference angle related to the angle in the third quadrant?

• They are unrelated

• They have different tangent values

• They have the same tangent value

• They are complementary

What is the final step to find the smallest positive angle in the third quadrant?

• Divide the reference angle by pi

• Multiply the reference angle by pi

• Add the reference angle to pi

• Subtract the reference angle from pi

What is the approximate value of the smallest positive angle passing through the given point?

• 3.43 radians

• 4.43 radians

• 5.43 radians

• 6.43 radians

Why does the calculator initially provide an angle in the first quadrant?

• Because the cosine function is negative

• Because the sine function is positive

• Because the tangent function is positive

• Because the tangent function is negative

What is the significance of both x and y being negative in the third quadrant?

• The tangent function value is positive

• The sine function value is positive

• The cosine function value is negative

• The tangent function value is negative