Exploring Adding and Subtracting Rational Expressions

The video tutorial covers solving trigonometric equations involving double angles, sine, cosine, cosecant, and cotangent. It explains how to find solutions using the unit circle and discusses the importance of considering the period of trigonometric functions. The tutorial also includes practice problems and emphasizes the need to find solutions within specified intervals.

What is the solution for sine 2x equals half within the interval 0 to 2π?

• π/6 and 5π/6

• 0 and π

• π/12 and 13π/12

• π/4 and 3π/4

What is the correct solution for x when solving the equation 2x = 5π/6 + 2πk?

• π/6 + πk

• 5π/12 + πk

• π/12 + πk

• 5π/6 + πk

How do you adjust the period when solving trigonometric equations?

• Divide by 2

• Subtract π/2

• Add 2πk

• Multiply by 2π

What is the reciprocal function used to solve cosecant equations?

• Cosine

• Sine

• Tangent

• Cotangent

In solving cosine 3x = 1/2, what are the initial solutions for theta?

• π/3 and 5π/3

• π/4 and 3π/4

• π/6 and 5π/6

• 0 and π

What happens to the solutions when you apply the transformation x = 3θ in trigonometric equations?

• They are divided by 3

• They are multiplied by 1/3

• They are multiplied by 3

• They remain unchanged

How do you convert a solution in radians to degrees?

• Multiply by 180/π

• Divide by 180/π

• Multiply by π/180

• None of the above

For the equation cotangent 3x = 1, how many solutions are expected between 0 and 360 degrees?

• Six

• Eight

• Four

• Two

What is the period of the tangent function?

• 4π

• π/2

• 2π

• π

Which angle is not typically used in solving half-angle trigonometric problems?

• π/2

• π/4

• π/6

• π/3