Trigonometric Functions and Properties

The video tutorial explains how to determine the sine and cosine of angle sums and differences using given trigonometric values in the fourth quadrant. It covers the process of finding missing trigonometric values using reference triangles and applying sum and difference identities to calculate the exact values of sine(a+b) and cosine(a-b).

In which quadrant are angles a and b located?

• First quadrant

• Second quadrant

• Third quadrant

• Fourth quadrant

What is the formula for sine of a sum of two angles?

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

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

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

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

What is the value of cosine(a) in terms of square root and fractions?

• Square root of 21 divided by 5

• Square root of 21 divided by 4

• Square root of 21 divided by 3

• Square root of 21 divided by 2

How do you determine the sign of y in the fourth quadrant?

• y is negative

• y is undefined

• y is positive

• y is zero

What is the simplified form of the square root of 8?

• 5 square root 2

• 4 square root 2

• 3 square root 2

• 2 square root 2

What is the formula for cosine of a difference of two angles?

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

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

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

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

What is the common denominator used in the calculations for sine(a+b) and cosine(a-b)?

• 12

• 15

• 10

• 18

What is the exact value of sine(a+b) in terms of square roots?

• Negative two plus square root 42

• Negative two minus square root 42

• Negative two plus two square root 42

• Negative two minus two square root 42

What is the exact value of cosine(a-b) in terms of square roots?

• Square root 21 minus four square root 2

• Square root 21 minus two square root 2

• Square root 21 plus four square root 2

• Square root 21 plus two square root 2

What is the prime factorization of 42?

• 2 x 4 x 7

• 2 x 3 x 7

• 2 x 3 x 5

• 3 x 4 x 7