Trigonometric Functions and Identities

The video tutorial explains how to determine the sine, cosine, and tangent of 2 theta given that tangent theta equals 2/3 and sine theta is less than zero. It involves identifying the correct quadrant, sketching a reference triangle, calculating the hypotenuse using the Pythagorean theorem, and applying double angle identities to find the required trigonometric functions. The tutorial concludes by verifying the results using different methods.

What is the given value of tangent theta in the problem statement?

• 1/2

• 2/3

• 3/4

• 4/5

In which quadrant is the terminal side of theta located?

• 1st Quadrant

• 3rd Quadrant

• 2nd Quadrant

• 4th Quadrant

What is the length of the hypotenuse in the reference triangle?

• √12

• √10

• √11

• √13

What is the value of sine theta calculated from the reference triangle?

• -2/√13

• -3/√13

• 2/√13

• 3/√13

Which identity is used to calculate sine of 2 theta?

• sin(2θ) = 2sinθcosθ

• sin(2θ) = 2tanθ/(1+tan²θ)

• sin(2θ) = sin²θ - cos²θ

• sin(2θ) = 1 - 2cos²θ

What is the calculated value of sine 2 theta?

• 11/13

• 10/13

• 13/13

• 12/13

Which identity is used to calculate cosine of 2 theta?

• cos(2θ) = 1 - 2sin²θ

• cos(2θ) = 2sinθcosθ

• cos(2θ) = cos²θ - sin²θ

• cos(2θ) = 2cos²θ - 1

What is the calculated value of cosine 2 theta?

• 4/13

• 6/13

• 3/13

• 5/13

What is the value of tangent 2 theta using the quotient identity?

• 10/5

• 13/5

• 11/5

• 12/5

Which method can be used to verify the result of tangent 2 theta?

• Reciprocal Identity

• Quotient Identity

• Pythagorean Identity

• Sum Identity