The line with equation a+2b=0 coincides with the terminal side of an angle 0 in standard position and cos 0 < 0. What is the value of sin0?

Question:

line x + 2y = 0 is end side of angle θ

and cos θ < 0

Answer: sin θ = √5/5

Step-by-step explanation:

cos θ < 0 means x < 0

Line is y = - x/2, slope - 1/2

Line intersects unit circle when x^2+y^2=1

x^2 + (-x/2) ^2 = 1

x^2 + x^2/4 = 1

5x^2/4 = 1

x = - √ (4/5) = - 2√ (1/5) = - 2√5/5

y = √5/5

x^2 = 4/5, y^2 = 1/5

sin θ is y value at intersection of line and unit circle, √5/5

The answer is √5/5 I took the test and got it right.