The equation, with a restriction on x, is the terminal side of an angle theta in standard position. negative 2xplusyequals0, xless than or equals0 give the exact values of the six trigonometric functions of theta.

tan(theta) = y/x = 2/1 = 2

sin(theta) = y/r = 2/√5

cos(theta) = x/r = 1/√5

tan(theta) = y/x = -2/√5

sin(theta) = y/r = -2/-1 = 2

cos(theta) = x/r = -1/√5

Step-by-step explanation:

-2x+y =0

y = 2x

So the ratio between y to x is:

y/x = 2

y:x = 2:1

For example, if x = 1, y = 2. Using this we'll get the hypotenus or the length of the terminal side as below

r = √(1^2 + 2^2) = √5

So the trigo for these are:

tan(theta) = y/x = 2/1 = 2

sin(theta) = y/r = 2/√5

cos(theta) = x/r = 1/√5

Another 3 trigo is when both x and y is negative (3rd quadrant)

Ex: x=-1, y=-2

r will be √5 as well

Hence

tan(theta) = y/x = -2/√5

sin(theta) = y/r = -2/-1 = 2

cos(theta) = x/r = -1/√5