11/25/22 - Sum and Difference Formulas,

Question 1

How do you find cos(θ) when θ is composed of angles a and b?

Answer 1

cos(a ± b) = cos(a)cos(b) ∓ sin(a)sin(b)

Question 2

How do you find sin(θ) when θ is composed of angles a and b?

Answer 2

sin(a ± b) = sin(a)cos(b) ± cos(a)sin(b)

Question 3

How do you find tan(θ) when θ is composed of angles a and b?

Answer 3

tan(a + b) = [tan(a) + tan(b)]/[1 - tan(a)tan(b)]

Question 4

How do you find sin(75 degrees) exactly?

Answer 4

Divide into special angles
sin(75) = sin(30 + 45)
sin(30 + 45) = sin(30)cos(45) + cos(30)sin(45)
Substitute values from the unit circle

Question 5

How do you find cos(105 degrees) exactly?

Answer 5

Divide into special angles
cos(105) = cos(60 + 45)
cos(60 + 45) = cos(60)cos(45) - sin(60)sin(45)
Substitute values from the unit circle

Question 6

How do you find tan(75 degrees) exactly?

Answer 6

Divide into special angles
tan(75) = tan(30 + 45)
tan(30 + 45) = [tan(30) + tan(45)]/[1 - tan(30)tan(45)]