Question

The line with equation a + 4b = 0 coincides with the terminal side of an angle θ in standard position and cos θ>0 . What is the value of sinθ ?

Answer 1

`-(√(17))/(17)`

Explanation:

as you can see I got the answer wrong so here's the right one

Answer 2

`(-1)/(√(17) )`

Step-by-step explanation

We have given that equation of line a+4b=0

⇒4b= -a

⇒
`b= (-a)/(4)`

slope of line =
`tan\theta =(P)/(B)= (-1)/(4)`

⇒
`tan\theta` is negative therefore it lies into 4th quadrant

By, Pythagoras theorem
`H^2=P^2+B^2`

by putting value of P= -1 & B=4

the value of
`H=√(17)`

with the given condition
`cos\theta>0`

i.e.
`\theta`∈ (3π/2, 2π)

now,
`sin\theta= (P)/(H)= (-1)/(√(17))`