How do you find the #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)# on the terminal side of an angle to calculate the trigonometric functions of the angle we use:

#sinalpha=y/r#

where #r# is the radius: #r=sqrt(x^2+y^2)#

Here we have:

#r=sqrt((-2)^2+(-5)^2)=sqrt(4+25)=sqrt(29)#

so

#sinalpha=(-5)/sqrt(29)=-(5sqrt(29))/29#