What I wish I knew about compound angles in trig

The video tutorial addresses common student difficulties in solving trigonometric equations, particularly with half and double angles. It explains how to solve these equations using the unit circle and graphical approaches, emphasizing the importance of understanding period changes in trigonometric graphs. The tutorial also covers methods to find all solutions for these equations, including the use of multiple angles and the impact of graph compression or stretching.

What is a common challenge students face when solving trigonometric equations with half and double angles?

• Understanding the unit circle

• Solving equations on an interval

• Finding the maximum value of a function

• Graphing linear equations

When solving sin(θ) = 1/2, which angles are solutions within the interval [0, 2π]?

• π/4 and 3π/4

• π/6 and 5π/6

• π/3 and 2π/3

• π/2 and 3π/2

How does the period of the sine graph change when solving sin(2θ) = 1/2?

• The period becomes 2π

• The period becomes 4π

• The period becomes π

• The period remains unchanged

What is the first step in finding solutions for sin(2θ) = 1/2?

• Add π to the angle

• Set 2θ equal to known solutions

• Multiply the angle by 2

• Divide the angle by 2

When dealing with half angles, what is the effect on the graph's period?

• The period is halved

• The period is tripled

• The period is doubled

• The period remains the same

What is the solution set for θ when solving sin(θ/2) = 1/2 within [0, 2π]?

• π/6 and 5π/6

• π/3 and 5π/3

• π/4 and 3π/4

• π/2 and 3π/2

What should you do after finding the initial solutions for a trigonometric equation with multiple angles?

• Add 2π to each solution

• Subtract π from each solution

• Multiply each solution by 2

• Adjust solutions to fit the interval