Solving Trigonometric Equations

The video tutorial explains how to solve the equation 5 sine 3x = 2 over a given interval by using substitution. Theta is introduced as 3x, and the equation is solved for theta using arcsine. The tutorial demonstrates how to find theta values in different quadrants and convert them to x values. It also explains the need to find additional solutions due to the periodic nature of the sine function. The tutorial concludes with a summary of all solutions for x within the interval.

What substitution is made to simplify the equation 5 sin(3x) = 2?

• theta = x

• theta = 5x

• theta = 3x

• theta = 2x

What is the equation after dividing both sides by 5?

• sin(theta) = 5/2

• sin(theta) = 1/5

• sin(theta) = 2/5

• sin(theta) = 3/5

Which mode should the calculator be in to find the arcsine of 2/5?

• Scientific mode

• Radian mode

• Degree mode

• Graphing mode

What is the approximate value of theta in the first quadrant?

• 3.1416 radians

• 0.4115 radians

• 1.5708 radians

• 2.730 radians

How is x calculated from theta?

• x = theta * 3

• x = theta / 3

• x = theta + 3

• x = theta - 3

Why are additional solutions for x needed?

• Because the sine function is constant

• Because the sine function is linear

• Because the sine function is periodic

• Because the sine function is quadratic

What is the period change when graphing y = sin(3x)?

• The period triples

• The period halves

• The period remains the same

• The period doubles

How many solutions for x are there over the interval?

• Two solutions

• Four solutions

• Six solutions

• Eight solutions

What is the approximate value of x for theta = 2.730 radians?

• 0.9100 radians

• 0.1372 radians

• 2.2316 radians

• 0.9100 radians

What is the purpose of finding coterminal angles?

• To find angles in the first quadrant

• To find angles in the third quadrant

• To find additional solutions within the interval

• To find angles in the second quadrant