Trigonometric Equations and Solutions

The video tutorial explains how to solve a trigonometric equation on the interval from 0 to 2π. It begins by transforming the equation into a quadratic form and then factoring it. The solutions for sine theta are found using the factored form, and the unit circle is used to identify the exact solutions. The tutorial concludes by summarizing the solutions in both radians and degrees, emphasizing the importance of the given interval.

What is the initial form of the trigonometric equation given in the tutorial?

• 2 sin^2(θ) - 3 sin(θ) = -1

• 2 sin^2(θ) - 3 sin(θ) = 0

• 2 sin^2(θ) + 3 sin(θ) = 1

• 2 sin^2(θ) + 3 sin(θ) = -1

What is the first step in transforming the trigonometric equation into a quadratic form?

• Divide both sides by 2

• Add 1 to both sides

• Multiply both sides by 2

• Subtract 1 from both sides

What are the factors of the quadratic equation after transformation?

• (2 sin(θ) - 1)(sin(θ) - 1)

• (2 sin(θ) + 1)(sin(θ) + 1)

• (2 sin(θ) - 1)(sin(θ) + 1)

• (2 sin(θ) + 1)(sin(θ) - 1)

What value of sin(θ) is obtained from the equation 2 sin(θ) - 1 = 0?

• 0

• 1/2

• 1

• -1/2

In which quadrants of the unit circle is sin(θ) positive?

• First and second

• Third and fourth

• First and fourth

• Second and third

What angle in radians corresponds to sin(θ) = 1/2 in the first quadrant?

• π/4

• π/3

• π/2

• π/6

What angle in radians corresponds to sin(θ) = 1/2 in the second quadrant?

• 5π/6

• 7π/6

• 3π/4

• 2π/3

What is the angle in radians where sin(θ) equals 1?

• 2π

• 3π/2

• π

• π/2

How many solutions are there for the equation on the interval from 0 to 2π?

• Four

• Three

• Two

• One

Why are the solutions given in radians?

• Because degrees are not used in trigonometry

• Because radians are easier to calculate

• Because radians are more accurate

• Because the interval is given in radians