sketch the angle in Theta standard position such that the terminal side of theta has equation for x + 3 y equals 0x less than zero find the valley of sin

sin(θ) = 1/√10 = 0.316

Step-by-step explanation:

Suppose that we have a point (x, y).

The angle between the positive x-axis and a ray that connects the origin with this point (x, y) is called θ, and will be true that:

sin(θ) = y/(√(x^2 + y^2))

cos(θ) = x/(√(x^2 + y^2))

tan(θ) = y/x

Here we want to find the angle θ defined by:

x + 3*y = 0

such that:

x < 0.

If we isolate y, so we get a linear equation:

3*y = -x

y = -x/3 = (-1/3)*x

In the image below you can see the graph of this equation, where we only look at the part where x < 0.

In the sketch, you can see that for any ordered pair with x negative we will get the same angle θ

So we can just evaluate our line with a negative value of x, so we get an ordered pair and we can use one of the above relations to find the value of sin(θ).

If we use x = -3, then:

y = (-1/3)*-3 = 1

Then we have the ordered pair (-3, 1)

So, if we use the sin relation above, we get:

sin(θ) = y/(√(x^2 + y^2)) =  1/( √((-3)^2 + 1^2))

sin(θ) = 1/(√(9 + 1)) = 1/(√10) = 1/√10

sin(θ) = 1/√10 = 0.316

answer: your answer is c

step-by-step explanation: