How to solve a trig equation with sine on both sides

The video tutorial explains how to solve a trigonometric equation involving sine. It begins by isolating the variable and using the unit circle to find specific angle solutions. The instructor discusses the constraints for solutions between 0 and 2π and explains how to find general solutions by adding multiples of 2π. The tutorial emphasizes understanding the unit circle and the significance of positive sine values in different quadrants.

What is the first step in solving the equation X = sqrt(3) - sin(X)?

• Multiply both sides by 2

• Add sin(X) to both sides

• Subtract sqrt(3) from both sides

• Divide both sides by sin(X)

After isolating sin(X), what is the next step to solve 2sin(X) = sqrt(3)?

• Add 2 to both sides

• Divide both sides by 2

• Subtract 2 from both sides

• Multiply both sides by 2

Which angles on the unit circle correspond to sin(X) = sqrt(3)/2?

• π/3 and 2π/3

• π/6 and 5π/6

• π/2 and 3π/2

• π/4 and 3π/4

In which quadrants is the sine function positive?

• 1st and 3rd

• 3rd and 4th

• 2nd and 4th

• 1st and 2nd

What is the significance of the interval [0, 2π] in trigonometric solutions?

• It is used to find the maximum value of sine

• It is the only interval where solutions exist

• It is irrelevant to trigonometric equations

• It represents one complete cycle of the sine function

What is the general solution for the equation sin(X) = sqrt(3)/2?

• X = π/2 + 2πk and X = 3π/2 + 2πk

• X = π/6 + 2πk and X = 5π/6 + 2πk

• X = π/4 + 2πk and X = 3π/4 + 2πk

• X = π/3 + 2πk and X = 2π/3 + 2πk

Why can we add multiples of 2π to the specific solutions?

• Because the unit circle repeats every 2π

• Because sine is a linear function

• Because it changes the value of sine

• Because it only applies to cosine