Trigonometric Identities and Solutions

The video tutorial explains how to solve the equation 4sin(x)cos(x) = √3 by using trigonometric identities. It begins by discussing why the zero product property cannot be applied and introduces the double angle identity to transform the equation. The instructor then demonstrates how to find solutions using the unit circle and symmetry, and finally calculates the solutions within the interval 0 to 2π.

What is the initial equation discussed in the video?

• 2 sin(x) cos(x) = √3

• sin(x) cos(x) = √3

• 4 sin(x) cos(x) = √3

• sin(x) + cos(x) = √3

Why can't the zero product property be applied to the initial equation?

• The equation is not set to zero.

• The equation is not a product.

• The equation is not quadratic.

• The equation is not linear.

Which trigonometric identity is introduced to help solve the equation?

• Pythagorean identity

• Product-to-sum identity

• Double angle identity

• Sum-to-product identity

How is the equation rewritten using the double angle identity?

• 2 sin(x) cos(x) = sin(2x)

• 2 sin(x) cos(x) = cos(2x)

• 4 sin(x) cos(x) = sin(2x)

• sin(x) cos(x) = sin(2x)

What are the angles found using the unit circle for the equation sin(2x) = √3?

• π/4 and 3π/4

• π/6 and 5π/6

• π/3 and 2π/3

• π/2 and π

What is added to the angles to find the general solutions?

• πn

• 2πn

• 3πn

• π/2n

What operation is performed to solve for x from 2x?

• Subtract 2

• Divide by 2

• Add 2

• Multiply by 2

What is the first specific solution for x within the interval [0, 2π]?

• π/4

• π/3

• π/2

• π/6

What is the second specific solution for x within the interval [0, 2π]?

• 4π/3

• 2π/3

• 5π/6

• 7π/6

What is the third specific solution for x within the interval [0, 2π]?

• 11π/6

• 4π/3

• 5π/3

• 7π/3