Cel R.

asked • 12/07/20# Trig Identities

Given 𝑠𝑖𝑛 𝛼 = 7 and 𝑠𝑖𝑛 𝛽 = 3, 𝛼 and 𝛽 in quadrant II, find 25 5

(a) 𝑠𝑖𝑛(𝛼 + 𝛽), (b) 𝑡𝑎𝑛(𝛼 + 𝛽), and (c) the quadrant of 𝛼 + 𝛽.

## 1 Expert Answer

John C. answered • 12/07/20

The Problem Solver

Given sin α = 7/25 in the second quadrant, cos α = -24 / 25

Given sin β = 3/5 in the second quadrant, cos β = -4 / 5

sin (α + β) = sin α cos β + cos α sin β = -100 / 125 = -4 / 5

cos (α + β) = cos α cos β - sin α sin β = 75 / 125 = 3 / 5

tan (α + β) = sin (α + β) / cos (α + β) = -4 / 3

Since the cosine of α + β is positive and the sine negative, α + β must be in the fourth quadrant.

Cel R.

Oops, I meant 𝑠𝑖𝑛 𝛼 = 7/25 and 𝑠𝑖𝑛 𝛽 =3/512/07/20

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John C.

Should read 𝑠𝑖𝑛 𝛼 = 7/25 and 𝑠𝑖𝑛 𝛽 =3/512/08/20