Trigonometric Functions and Identities

The video tutorial covers the sum and difference formulas for sine, cosine, and tangent functions. It demonstrates how to use these formulas to evaluate specific angles, such as sine 75 degrees, sine 15 degrees, cosine 7π/12, tangent π/12, and tangent 23π/12. The tutorial also explains the importance of knowing the unit circle and special triangles, like the 30-60-90 and 45-45-90 triangles, and introduces the SOHCAHTOA mnemonic for understanding trigonometric ratios.

Which formula would you use to find the sine of the sum of two angles?

• sine(a) * sine(b) + cosine(a) * cosine(b)

• sine(a) * sine(b) - cosine(a) * cosine(b)

• sine(a) * cosine(b) + cosine(a) * sine(b)

• cosine(a) * cosine(b) - sine(a) * sine(b)

What is the sine of 30 degrees using the 30-60-90 triangle?

• 1

• √2/2

• 1/2

• √3/2

How do you convert an angle from radians to degrees?

• Multiply by π/180

• Multiply by 180/π

• Multiply by 360/π

• Multiply by π/360

What is the cosine of 60 degrees?

• 1

• √2/2

• 1/2

• √3/2

Which formula is used to find the tangent of the difference of two angles?

• tan(a) + tan(b) / 1 + tan(a)tan(b)

• tan(a) + tan(b) / 1 - tan(a)tan(b)

• tan(a) - tan(b) / 1 + tan(a)tan(b)

• tan(a) - tan(b) / 1 - tan(a)tan(b)

What is the tangent of 45 degrees?

• 0

• √3

• √3/3

• 1

What is the result of multiplying a number by its conjugate?

• The difference of squares

• The sum of squares

• The product of squares

• The quotient of squares

What is the reference angle for 120 degrees in the unit circle?

• 60 degrees

• 90 degrees

• 45 degrees

• 30 degrees

How do you simplify a complex fraction?

• Divide the numerator by the denominator

• Subtract the numerator from the denominator

• Add the numerator and denominator

• Multiply the numerator and denominator by the same number

What is the tangent of 225 degrees?

• 0

• √3

• -1

• 1