How do you find the $sin θ$ $sintheta$ for an angle in standard position if the terminal side passes through the point (-2, -5)?

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Answer 1 · 2017-01-30T07:45:29

See explanation.

If we have a point $P = (x, y)$ $P=(x,y)$ on the terminal side of an angle to calculate the trigonometric functions of the angle we use:

$sin α = \frac{y}{r}$ $sinalpha=y/r$

where $r$ $r$ is the radius: $r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$

Here we have:

$r = \sqrt{{(- 2)}^{2} + {(- 5)}^{2}} = \sqrt{4 + 25} = \sqrt{29}$ $r=sqrt((-2)^2+(-5)^2)=sqrt(4+25)=sqrt(29)$

so

$sin α = \frac{- 5}{\sqrt{29}} = - \frac{5 \sqrt{29}}{29}$ $sinalpha=(-5)/sqrt(29)=-(5sqrt(29))/29$