How to solve an equation with cosine

The video tutorial explains how to solve cosine equations using both the unit circle and graphing methods. It begins with an introduction to solving graphs and then delves into using the unit circle to find specific angles where cosine equals 1/2. The tutorial continues by graphing the cosine function to visually identify solutions between 0 and 2π. Finally, it discusses finding all possible solutions by adding multiples of 2π, emphasizing the concept of infinite solutions in trigonometric functions.

What is the initial equation the teacher wants to solve using the unit circle?

• cos(X) = 2

• 2cos(X) = 1/2

• 2sin(X) = 1/2

• tan(X) = 1/2

Which angles are identified as solutions for cosine equals 1/2 on the unit circle?

• π/4 and 3π/4

• π/3 and 5π/3

• π/6 and 5π/6

• π/2 and 3π/2

What is the period of the cosine function?

• π

• 2π

• π/2

• 3π

How does the teacher suggest finding where cosine equals 1/2 on the graph?

• By drawing a line at y = 1/2

• By drawing a line at y = -1/2

• By drawing a line at y = 0

• By drawing a line at y = 1

What concept explains why solutions continue beyond one period?

• Amplitude

• Symmetry

• Frequency

• Periodicity

What is added to each solution to find all possible solutions?

• 3π

• 2π

• π/2

• π

What is the significance of adding 2π to the solutions?

• It accounts for the periodic nature of the cosine function.

• It reflects the graph over the x-axis.

• It shifts the graph vertically.

• It changes the amplitude of the graph.