Trigonometric Equations and Solutions

The video tutorial covers solving trigonometric equations involving double angles. It begins with isolating the trigonometric function and using the unit circle to find solutions. The focus then shifts to solving for two theta and finding all possible solutions within a specified range. The tutorial explains the concept of all solutions and demonstrates calculating additional solutions using different values of n. The session concludes with a graphical representation to enhance understanding.

What is the first step in solving a trigonometric equation with a double angle?

• Subtract a constant from both sides

• Add a constant to both sides

• Isolate the trigonometric function

• Multiply both sides by 2

When isolating the trigonometric function, what operation is performed after adding 3 to both sides?

• Subtract 4

• Multiply by 4

• Add 4

• Divide by 4

What is the result of taking the square root of both sides in the equation 4cos²(2θ) = 3?

• cos(2θ) = ±3/2

• cos(2θ) = ±√3/2

• cos(2θ) = ±2/3

• cos(2θ) = ±√2/3

Which angle on the unit circle corresponds to cos(θ) = √3/2?

• π/4

• π/3

• π/2

• π/6

What are the initial solutions for θ when cos(θ) = ±√3/2?

• π/2, π, 3π/2, 2π

• π/3, 2π/3, 4π/3, 5π/3

• π/4, 3π/4, 5π/4, 7π/4

• π/6, 5π/6, 7π/6, 11π/6

How do you solve for 2θ if you have solutions for θ?

• Divide by 2

• Multiply by 2

• Subtract 2

• Add 2

What is the range of solutions we are interested in for 2θ?

• 0 to 2π

• 0 to 4π

• 0 to 3π

• 0 to π

What is the equivalent of 2π in terms of a denominator of 12?

• 12π/12

• 24π/12

• 18π/12

• 30π/12

How do you find additional solutions using n values?

• Add multiples of π

• Add multiples of π/2

• Add multiples of π/6

• Add multiples of 2π

What is the next solution after 7π/12 when n=1?

• 11π/12

• 9π/12

• 15π/12

• 13π/12