Understanding Cosine and Sine in Trigonometry

The video tutorial explains how to express cosine of (X + 5π/6) using sine and cosine functions. It introduces the sum and difference identity for cosine, applies it to specific values, and evaluates the trigonometric functions using both a reference triangle and the unit circle. The tutorial concludes by verifying the results and ensuring the correct trigonometric values are obtained.

What is the main goal of the problem discussed in the video?

• To determine the value of X

• To express cosine of (X + 5π/6) using sine and cosine

• To calculate the tangent of X

• To find the value of sine X

Which identity is used to express cosine of (X + 5π/6)?

• Double angle identity

• Pythagorean identity

• Sum and difference identity

• Half angle identity

What is the degree equivalent of 5π/6 radians?

• 90 degrees

• 120 degrees

• 150 degrees

• 180 degrees

In a 30-60-90 triangle, what is the length of the hypotenuse if the short leg is 1?

• 1

• 3

• √3

• 2

Why is the adjacent side negative in the reference triangle for 5π/6?

• Because it is in the third quadrant

• Because it is in the second quadrant

• Because it is in the first quadrant

• Because it is in the fourth quadrant

What is the cosine of 5π/6 using the reference triangle?

• 1/2

• -1/2

• √3/2

• -√3/2

What is the sine of 5π/6 using the reference triangle?

• 1/2

• √3/2

• -√3/2

• -1/2

On the unit circle, what does cosine θ represent?

• The y-coordinate

• The radius

• The angle

• The x-coordinate

On the unit circle, what does sine θ represent?

• The y-coordinate

• The radius

• The angle

• The x-coordinate

What is the final expression for cosine of (X + 5π/6) using sine and cosine?

• sin(X) * cos(5π/6) + cos(X) * sin(5π/6)

• cos(X) * cos(5π/6) - sin(X) * sin(5π/6)

• sin(X) * cos(5π/6) - cos(X) * sin(5π/6)

• cos(X) * cos(5π/6) + sin(X) * sin(5π/6)