Trigonometric Functions and Formulas

The video tutorial covers the derivation and application of power reducing and half angle formulas for sine, cosine, and tangent. It includes examples of calculating trigonometric values for specific angles using these formulas, such as cosine of 15 degrees, sine of 22.5 degrees, and tangent of 75 degrees. The tutorial emphasizes understanding the formulas and applying them to solve trigonometric problems.

What is the half-angle formula for sine?

• sin(θ/2) = ±√(1 + sinθ)/2

• sin(θ/2) = ±√(1 - sinθ)/2

• sin(θ/2) = ±√(1 - cosθ)/2

• sin(θ/2) = ±√(1 + cosθ)/2

Which formula represents the half-angle for cosine?

• cos(θ/2) = ±√(1 - sinθ)/2

• cos(θ/2) = ±√(1 + cosθ)/2

• cos(θ/2) = ±√(1 - cosθ)/2

• cos(θ/2) = ±√(1 + sinθ)/2

How is the half-angle formula for tangent derived?

• Using the sine and cosine half-angle formulas

• Using the sine and tangent half-angle formulas

• Using the cosine and tangent half-angle formulas

• Using the sine and cotangent half-angle formulas

What is the value of cosine 15 degrees using the half-angle formula?

• √2 + √3 / 2

• √2 - √3 / 2

• √6 + √2 / 4

• √6 - √2 / 4

In which quadrant is 15 degrees located?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What is the exact value of sine 22.5 degrees?

• √2 + √2 / 2

• √2 - √2 / 2

• √3 + √2 / 2

• √3 - √2 / 2

Which quadrant is 22.5 degrees in?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What is the reference angle for cosine 150 degrees?

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

What is the exact value of tangent 75 degrees?

• 2 + √3

• 1 - √3

• 2 - √3

• 1 + √3

What is the sign of cosine in the second quadrant?

• Negative

• Positive

• Undefined

• Zero