Question

Suppose α is an angle in standard position whose terminal side lies in Quadrant III. If tan α = 2 3 , find the value of sin α?

Answer 1

`sin(alpha) = -0.999`

Explanation:

`tan alpha = 23` ; `alpha = 87.5^o +n(180)`

Standard position means one side is along the x-axis, with vertex at the origin.
Terminal side in Quadrant III is `180 <= alpha <= 270`

`alpha = 87.5^o +(180) = 267.5^0`

`sin(267.5) = -0.999`

https://mathbitsnotebook.com/Algebra2/TrigConcepts/TCStandardPosition.html

Answer 2

`sin a = - 23/sqrt530`

Explanation:

tan a = 23 --> `cot a = 1/23`
`sin^2 a = 1/(1 + cot^2 a) = 1/(1 + 1/529) = 529/530`
`sin a = +- 23/sqrt530`
Since a in in Quadrant 3, sin a is negative
`sin a = - 23/23.05 = - 0.999`