Solving Equations Involving Multiple Angles: Using Trig Identities and Graph Transformations

The video tutorial covers essential trigonometry skills, including solving equations using trigonometric identities, graph transformations, and the CAST diagram. It provides detailed examples of solving equations involving multiple angles, such as Cos 2 Theta and Sin 3 Theta, emphasizing the importance of understanding graph transformations to determine the number of solutions.

What are the key areas of confidence needed for solving trigonometric equations?

• Graph transformations and solving equations

• Solving equations, using trig identities, graph transformations, and CAST diagram

• Only solving equations and using trig identities

• Using trig identities and CAST diagram

What is the first step in solving the equation Cos 2θ = √3/2?

• Divide by 2

• Multiply both sides by 2

• Take the inverse cosine of both sides

• Add 1 to both sides

How many cycles does the graph of Cos 2θ complete between 0 and 360 degrees?

• Three cycles

• Four cycles

• Two cycles

• One cycle

What transformation occurs to the graph of sin(3θ) in the equation 2sin(3θ) - 1 = 0?

• Stretch in the Y-axis by a factor of 1/3

• Stretch in the X-axis by a factor of 1/3

• Stretch in the X-axis by a factor of 3

• Stretch in the Y-axis by a factor of 3

How many cycles does the graph of sin(3θ) complete between 0 and 360 degrees?

• Four cycles

• Three cycles

• Two cycles

• One cycle

What is the importance of understanding graph transformations in solving trigonometric equations?

• To establish multiple values for θ

• To avoid using the CAST diagram

• To simplify the equations

• To determine the number of cycles in a graph

What is the role of the CAST diagram in solving trigonometric equations?

• To avoid using trig identities

• To solve equations directly

• To establish multiple values for θ

• To visualize graph transformations