Trigonometric Equations and Identities

The video tutorial explains how to solve a trigonometric equation by converting cotangent to sines and cosines, manipulating fractions, factoring, and using double angle identities. It demonstrates solving for variables using the unit circle, providing solutions for x within a specified interval.

What is the first step in solving the trigonometric equation given in the video?

• Use the unit circle

• Multiply both sides by sine x

• Convert cotangent to sines and cosines

• Apply double angle identities

Why do we need a common denominator when rewriting the equation?

• To factor the equation

• To eliminate the fraction

• To apply the unit circle

• To simplify the equation

What is the greatest common factor that is factored out in the equation?

• Sine x

• Cosine x

• Cotangent x

• Tangent x

Which identity is used to simplify the expression involving two trigonometric functions?

• Pythagorean identity

• Sum and difference identities

• Half angle identity

• Double angle identity

What substitution is made to solve the equation involving sine 2x?

• Let t equal x

• Let t equal 2x

• Let t equal sine x

• Let t equal cosine x

How do we find the solutions for x using the unit circle?

• By finding where the y-coordinate is zero

• By finding where the y-coordinate is one

• By finding where the x-coordinate is one

• By finding where the x-coordinate is zero

What is the interval for t when solving sine t equals one?

• 0 to 2π

• 0 to 3π

• 0 to π

• 0 to 4π

What is the first solution for x found in the video?

• π/4

• π/2

• 5π/4

• 3π/2

How many total solutions for x are found within the interval?

• Two

• Five

• Three

• Four

What is the final solution for x mentioned in the video?

• π/2

• 5π/4

• 3π/2

• π/4