Question

If terminal side of angle t goes through (-5/13,12/13) what is sin(t)

Answer 1

Given the point P(-5/13,12/13)

the angle t is

then

since we know x and y values (-5/13,12/13) we can solve theta

where

Opp = -5/13

Adj = 12/13

`tan(\theta)=(Opp)/(Adj)`
`tan(\theta)=((-5)/(3))/((12)/(13))`
`tan(\theta)=(-5*13)/(3*12)`
`tan(\theta)=(-65)/(36)`
`\theta=ArcTan((-65)/(36))`
`\theta=61.02°`

Adding the 90° of the first quadrant

The angle t is

`t=61.02+90`
`t=151.02`

to rads

`t=(151.02\pi)/(180)`

then sin t

`sin(t)=0.48450`