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

Answer:

$\frac{-1}{\sqrt{17} }$

Step-by-step explanation

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

⇒4b= -a

⇒$b= \frac{-a}{4}$

slope of line = $tan\theta =\frac{P}{B}= \frac{-1}{4}$

⇒ $tan\theta$ 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 $H=\sqrt{17}$

with the given condition $cos\theta>0$

i.e. $\theta$∈ (3π/2, 2π)

now, $sin\theta= \frac{P}{H}= \frac{-1}{\sqrt{17}}$