Using the addition of two angles and tangent

The video tutorial explains how to find the tangent of an angle not on the unit circle by expressing it as a sum of two angles. It uses the tangent sum formula to calculate the tangent of these angles. The tutorial then demonstrates how to find the tangent values using the unit circle and simplifies the resulting expression by multiplying with the conjugate to eliminate radicals.

Why is it necessary to express an angle as a sum or difference of known angles on the unit circle?

• To convert the angle to degrees

• To find the exact value of the angle

• To use the tangent sum formula

• To simplify the calculation of sine and cosine

What is the formula for the tangent of the sum of two angles?

• tan(U + V) = tan(U) + tan(V)

• tan(U + V) = (tan(U) + tan(V)) / (1 - tan(U)tan(V))

• tan(U + V) = (tan(U) - tan(V)) / (1 + tan(U)tan(V))

• tan(U + V) = tan(U) - tan(V)

What is the tangent of 3π/4?

• 1

• -1

• √3

• -√3

How do you simplify the expression for tangent when it involves a radical in the denominator?

• Add the radical to the numerator

• Divide by the radical

• Multiply by the conjugate

• Subtract the radical from the denominator

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

• The sum of the squares

• The difference of the squares

• The product of the numbers

• The square of the number

What is the final simplified form of the tangent expression in the video?

• 1 - √3

• 1 + √3

• -1 - √3

• -1 + √3

Why is it important to rationalize the denominator in mathematical expressions?

• To simplify the numerator

• To convert the expression to a fraction

• To eliminate radicals from the denominator

• To make the expression easier to read