Chapter 2: Sine and Cosine

Question 1

sin(ø) =3/5
ø is in Q II
find cos(ø)

Answer 1

cos(ø) = -4/5

[x² + y² = 1]
[cos²(ø) + sin²(ø) = 1]
[cos²(ø) + (3/5)² = 1]
[cos² + 9/25 = 1]
[cos² = 16/25]
[cos = √16/√25]
[cos = -4/5] [negative because cos(ø) is in Q II]

Question 2

sin(ø) = -7/25
ø is in Q IV
what is cos(ø)?

Answer 2

cos(ø) = 24/25

[x² + y² = 1]
[cos²(ø) + sin²(ø) = 1]
[cos²(ø) + (-7/25)² = 1]
[cos²(ø) + 49/625 = 1]
[cos²(ø) = 576/625]
[cos(ø) = √576/√625]
[cos(ø) = 24/25]
[positive because cos(ø) is in QI]