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

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. -82562234434584

step-by-step explanation:

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²