Trigonometric Functions and Identities

The video tutorial explains how to solve the trigonometric equation sine 2x = 2 cosine squared x over a given interval. It covers using the double angle identity for sine, factoring the equation, and finding solutions where cosine x equals zero and tangent x equals one. The tutorial also reviews how to express all solutions to the equation using the unit circle.

What is the initial equation that needs to be solved in the video?

• Sine X = Cosine X

• Sine 2X = 2 Cosine Squared X

• Tangent X = 1

• Cosine X = 0

Which identity is used to replace Sine 2X in the equation?

• Sum and Difference Identity

• Pythagorean Identity

• Half Angle Identity

• Double Angle Identity

What is the result of factoring the equation after setting it to zero?

• 2 Sine X = 0

• Cosine X = Sine X

• 2 Cosine X (Cosine X - Sine X) = 0

• Sine X = 0

Which angles have a cosine function value of zero on the unit circle?

• Pi/3 and 2Pi/3

• Pi/4 and 5Pi/4

• Pi/2 and 3Pi/2

• 0 and Pi

What is the condition for tangent to equal one on the unit circle?

• X and Y coordinates are opposite

• Y coordinate is zero

• X coordinate is zero

• X and Y coordinates are equal

At which angles does tangent equal one?

• Pi/4 and 5Pi/4

• Pi/3 and 2Pi/3

• 0 and Pi

• Pi/2 and 3Pi/2

How are all solutions for cosine X equals zero expressed?

• X = 0 + nPi

• X = Pi/3 + nPi

• X = Pi/4 + nPi

• X = Pi/2 + nPi

How are all solutions for tangent X equals one expressed?

• X = Pi/3 + nPi

• X = Pi/4 + nPi

• X = 0 + nPi

• X = Pi/2 + nPi

What are the four solutions found within the given interval?

• Pi/3, 2Pi/3, 4Pi/3, 5Pi/3

• Pi/4, 3Pi/4, 5Pi/4, 7Pi/4

• 0, Pi, Pi/2, 3Pi/2

• Pi/2, 3Pi/2, Pi/4, 5Pi/4

What is the interval within which the solutions are found?

• Pi to 2Pi

• Pi/2 to 3Pi/2

• 0 to 2Pi

• 0 to Pi