Question

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?

Answer 1

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

Answer 2

In this exercise we have to use the given equation and thus calculate the intersection value:

$sin (\theta) = \sqrt{5/5}$

So knowing that you were informed:

Line x + 2y = 0 is end side of angle θ and  cos θ < 0 means x < 0.  Line is y = -x/2, slope -1/2 and the  Line intersects unit circle when :

$x^2+y^2=1\\x^2 + (-x/2)^2 = 1\\x^2 + x^2/4 = 1\\5x^2/4 = 1\\x = -\sqrt{4/5} = -2\sqrt{1/5} = -2\sqrt{5/5}\\y = \sqrt{5/5}\\x^2 = 4/5, y^2 = 1/5$

$sin(\theta)$  is y value at intersection of line and unit circle, $\sqrt{5/5}$

See more about intersection at brainly.com/question/12089275