Understanding Secant and Reference Angles

The video tutorial explains how to find the two smallest positive angles that satisfy the condition where the secant of angle a is less than zero, and the reference angle is 1.0687 radians. It covers the properties of the secant function, its relation to cosine, and how the sign of x affects the secant value. The tutorial guides through finding the smallest positive angle in the second quadrant and the second smallest in the third quadrant, using the reference angle. Finally, it provides decimal approximations for these angles.

What is the reference angle given in the problem?

• 4.21 radians

• 2.0729 radians

• 1.0687 radians

• 3.14 radians

What is the relationship between secant and cosine?

• Secant is the reciprocal of sine

• Secant is the reciprocal of tangent

• Secant is the same as cosine

• Secant is the reciprocal of cosine

In which quadrants is secant negative?

• Third and fourth

• First and fourth

• Second and third

• First and second

How do you find the smallest positive angle in the second quadrant?

• Add the reference angle to pi

• Subtract the reference angle from pi

• Multiply the reference angle by pi

• Divide pi by the reference angle

What is the smallest positive angle in the second quadrant?

• 2.0729 radians

• 1.0687 radians

• 4.21 radians

• 3.14 radians

How do you find the second smallest positive angle in the third quadrant?

• Divide pi by the reference angle

• Multiply the reference angle by pi

• Subtract the reference angle from pi

• Add the reference angle to pi

What is the second smallest positive angle in the third quadrant?

• 2.0729 radians

• 1.0687 radians

• 3.14 radians

• 4.21 radians

What is the formula for angle a if it terminates in the second quadrant?

• a = 2pi + reference angle

• a = pi - reference angle

• a = 2pi - reference angle

• a = pi + reference angle

What is the formula for angle a if it terminates in the third quadrant?

• a = pi + reference angle

• a = pi - reference angle

• a = 2pi - reference angle

• a = 2pi + reference angle

What are the decimal approximations for the two angles found?

• 2.0729 and 3.14 radians

• 1.0687 and 3.14 radians

• 2.0729 and 4.21 radians

• 1.0687 and 4.21 radians