Trigonometric Equations and Angles

The video tutorial explains how to solve equations involving cosine by isolating the cosine term and using the unit circle to find corresponding x values. It highlights the importance of understanding coterminal angles and their multiples in finding all possible solutions.

What is the first step in solving a trigonometric equation?

• Isolating the variable

• Undoing addition or subtraction

• Multiplying both sides by a constant

• Finding the unit circle

After undoing addition or subtraction, what is the next step?

• Finding the unit circle

• Adding a constant to both sides

• Isolating the variable

• Undoing multiplication or division

What value of cosine are we trying to find on the unit circle?

• 1

• 0

• Negative one-half

• Positive one-half

Which angles on the unit circle correspond to a cosine value of negative one-half?

• π/4 and 3π/4

• 2π/3 and 4π/3

• π/3 and 2π/3

• π/6 and 5π/6

What is the cosine value at the angle 2π/3?

• 0

• Negative one

• 1/2

• Negative one-half

What is the cosine value at the angle 4π/3?

• Negative one-half

• Negative one

• 1/2

• 0

What is a coterminal angle?

• An angle that is a multiple of π

• An angle that is a multiple of 45 degrees

• An angle that shares the same terminal side as another angle

• An angle that is a multiple of 90 degrees

How do you find coterminal angles?

• By adding or subtracting multiples of π

• By adding or subtracting multiples of 2π

• By dividing by a constant

• By multiplying by a constant

What is the general solution for x when cos(x) = -1/2?

• x = 2π/3 + 2πn and x = 4π/3 + 2πn

• x = π/3 + 2πn and x = 5π/3 + 2πn

• x = π/4 + 2πn and x = 3π/4 + 2πn

• x = π/6 + 2πn and x = 5π/6 + 2πn

Why do we add multiples of 2π to the angles?

• To simplify the equation

• To find the unit circle

• To isolate the variable

• To find all possible solutions