Solving Trigonometric Equations

The video tutorial explains how to solve the equation sine x + 0.36 = 0 within the interval from 0 to 2π radians. It involves isolating sine x, using inverse sine to find solutions, and employing a calculator to determine angles. The tutorial also covers finding coterminal angles within the specified interval and verifying solutions by checking sine values.

What is the first step in solving the equation sin(x) + 0.36 = 0?

• Divide both sides by 0.36

• Subtract 0.36 from both sides

• Add 0.36 to both sides

• Multiply both sides by 0.36

Why is a calculator necessary to solve sin(x) = -0.36?

• Because the angle is a special angle

• Because the angle is in the first quadrant

• Because the angle is not on the unit circle

• Because the angle is greater than 2π

What is the range of the inverse sine function?

• -π/2 to π/2

• 0 to π

• -π to π

• 0 to 2π

What is the reference angle for the solution given by the calculator?

• 1.3683 radians

• 0.3683 radians

• π radians

• 2π radians

How do you find the first solution in the interval [0, 2π)?

• Add the reference angle to 2π

• Subtract the reference angle from 2π

• Add the reference angle to π

• Subtract the reference angle from π

In which quadrant is the second solution located?

• Fourth quadrant

• First quadrant

• Second quadrant

• Third quadrant

How is the second solution calculated?

• By adding the reference angle to 2π

• By subtracting the reference angle from π

• By subtracting the reference angle from 2π

• By adding the reference angle to π

What is the approximate value of the first solution?

• 3.5099 radians

• 2.9149 radians

• 5.9149 radians

• 0.3683 radians

What is the approximate value of the second solution?

• 2.9149 radians

• 3.5099 radians

• 5.9149 radians

• 0.3683 radians

What should the sine value of the solutions be approximately?

• 0.36

• -0.36

• 0.3683

• -0.3683