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

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

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step-by-step explanation: