Solving Trigonometric Equations

The video tutorial explains how to solve a trigonometric equation on the interval from 0 to 2π, closed on 0 and open on 2π. It involves adding 0.32 to both sides of the equation and using a calculator to find the sine of the angle. The tutorial covers the use of inverse sine to simplify the equation and find the angle X. It also discusses the importance of the unit circle and the sine function's positivity in the first and second quadrants. The video demonstrates how to find solutions in both quadrants and calculate the angle in the second quadrant by subtracting the reference angle from π.

What is the interval on which we are solving the trigonometric equation?

• 0 to 2π, closed on 0 and open on 2π

• 0 to 2π, open on both ends

• 0 to π, closed on both ends

• 0 to π, open on both ends

What operation is performed to both sides of the equation to isolate sine x?

• Divide by 0.32

• Subtract 0.32

• Add 0.32

• Multiply by 0.32

Which function is used to solve for the angle x in the equation sine x = 0.32?

• Inverse Cosine

• Cosine

• Tangent

• Inverse Sine

In which quadrants is the sine function positive?

• First and Second

• First and Fourth

• Second and Third

• Third and Fourth

What is the approximate value of the angle x in the first quadrant?

• 2.326 radians

• 3.326 radians

• 1.326 radians

• 0.326 radians

What is the reference angle used to find the second solution in the second quadrant?

• 0.326 radians

• 1.326 radians

• 3.326 radians

• 2.326 radians

How do you calculate the angle in the second quadrant with the same sine value?

• Divide the reference angle by π

• Add the reference angle to π

• Multiply the reference angle by π

• Subtract the reference angle from π

What is the approximate value of the angle in the second quadrant?

• 4.816 radians

• 3.816 radians

• 2.816 radians

• 1.816 radians

Why is it important to ensure all solutions are found within the given interval?

• To simplify the equation

• To ensure the calculator is in the correct mode

• To avoid missing any potential solutions

• To make the equation more complex

What should you check on your calculator before solving trigonometric equations?

• Scientific mode

• Radian mode

• Degree mode

• Graphing mode