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when you use the measures from the unit circle with the ratios, since the hypotenuse is 1,  the sin is sin(y/1) and the cos is cos(x/1).

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Cos, adjacent / hypotenuse, X
Sin, opposite / hypotenuse, Y
Tan, opposite / adjacent, Y/X

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on the unit circle, the hypotenuse is always one.

sin is opposite over hypotenuse, so you are doing y/1. because the hypotenuse is always one, sin is the y coordinate.

cos is adjacent over hypotenuse, so you are doing x/1. because the hypotenuse is always one, cos is the x coordinate.

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The hypotenuse is always one. And since since is opp/hyp,  it will always be the y coordinate cause it's y/1

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trig ratios are defined as sohcahtoa because it all makes sense on the unit circle when the hypotenuse is always one and x and y being divided by one will always get you x or y.

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sin= Y
cos= X
tan= Y/X
csc= 1/Y
sec= 1/X
cot= X/Y
the trig functions can be represented at coordinates because sin= opp/ hyp and in the unit circle the hypotenuse is always one therfore sin= opp/ 1. then you find the opposite side from the angle that you are looking for, in the case of sin, this side will always lay along the Y axis

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In the unit circle, the hypotenuse is 1, so sin (opp/hyp) is y/1 and cos (adj/hyp) is x/1

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Hypotenuse is always one and sin is opp/hyp. The unit shows that they are opposite

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The hypotenuse is always one and sin is opp/hyp. We can see from the unit circle that they are the opposite, y/1

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because the hypotenuse is 1 then SIN is opp/hyp or y/1 and cos is adj/hyp or x/1

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The H in SOHCAHTOA is the hyp which is always 1, so that means sin which is OPP/HYP = X/1, and cos which is ADJ/HYP = Y/1.

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in the unit circle, the hypotenuse is always one, and using the hypotenuse, we are able to find sin and cos, because sin is y/1 and cos is x/1, which just leaves you with the lengths of the legs of the triangle

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In the unit circle sin=x cos= y and tan= y/x and for example sin can be written as opp/hyp. And the hypotenuse always equal 1.

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Since the hypotenuse is always 1, we can say that sin is opp/hyp because sin is y and cos is adj/hyp because cos is x.

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The hypotenuse of a reference triangle on the unit circle is always 1, and anything divided by 1 is itself. Sin is just y because y/1 = y. Cos is x/1, which is x.

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In a unit circle, the radius is always one unit, or one. If you are trying to find the trig ratio of a given angle and draw a right triangle with the right angle on the initial side, the side opposite the right angle, the hypotenuse,  is equal to the length of the radius--1. When trying to figure out the trig ratios, the implementation of the knowledge that the hyp equals 1 comes in handy. The sine value, opp over hyp, can be also be written as y over hyp, since the opposite side is vertical, but also could be further restated as y over 1, or simply y, because anything divided by 1 is just itself. The cosine value, adj over hyp, can be rewriiten as x over 1 or just x, since the adj side is horizontal, and corresponds to the x coordinate. Therefore, the sin and cos values in a unit circle are equal to the y and x values, respectively. The tan ratio, opp over adj, is the same as y over x (vertical and horizontal.)

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Because the hypotenuse is one and these are right triangles,  these equations can be used to get certain points of this deck such as cos for x and sin for y.

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The hypotenuse is always 1,  so when trying to find Sin (y) you will always solve got y/1 or for cos it will always be x/1

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The hypotenuse will always be one, making sin and cos always be y/1 or x/1

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Hypotenuse is always 1. Sin is opposite/hypo so it will be y/1.

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When refrecing to the unit circle we always know that our hypothenuse is 1, so when solving for sin (Opp/Hyp) it is y/1

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It is because the hypotenuse in the unit circle is always 1, and for "Y", its sin which is opposite over hypotenuse which is Y. so the Y side is the opposite whereas the X side is the adjacent side.

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Since the hypotenuse is 1, then (SOH) is sin = y/1, and
(CAH) is cos = x/1

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Within the unit circle the radius of an angle or a triangle will always be just 1. So, knowing this we can determine that if we made a right triangle out of an angle in the circle, the x coordinate would just be x/1 as in adj/hyp for cos. The same idea applies to sin as y would just be y/1, as in opp/hyp.

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The hypotenuse is always going to be one. and sin is opp/hyp. since the hypotenuse is 1, sin equals your opposite

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In the unit circle, we always know the hypotenuse is going to equal 1. Because sin is opp/hyp and cos is adj/hyp we are always able to determine their values.

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In the unit circle, the hypotenuse will always be one but the X and Y values may vary depending on the sin (Y) and cos(X).

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Knowing that the hypotenuses is always 1, the sides of the triangle can be expressed as x and y coordinates. For example sine is opp/hyp and if the hypotenuse is always 1 and sine is equal to y then your answer would be the y coordinate.

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Sohcahtoh is
Sin= opposite/hypotenuse
Cos=Adjacent/hypotenuse
Tan= Opposite/hypotenuse

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since the hype = 1, sin = y and cos = x because SOH would be sin = opp/hyp which would be y/1 and cos would be x because cos = adj/hyp which would be x/1. if the numerator is over one, the answer will be the numerator making y/1 y and x/1 x.

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According to the unit circle, we know the hypotenuse is always 1. So when we're trying to find sin (SOH), it is y/1.

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The unit circle works because you can create 90 degree triangles inside it; which allows us to work with the special triangles from Geometry. X represents cos because it is the same thing as saying adj./hyp. which in the UNIT circle means x/1. And the same thing for sin; sin equals y, because it is the same thing as saying opp./hyp. which in the unit circle means y/1.

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In a unit circle, sin being the x value that can be explained as opp./ hypotenuse or y/1 and cosine is the y value that can be written as adj/hypotenuse or x/1. The hypotenuse is equal to one. The coordinates represent the length of each radian/degree on the unit circle.

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First of all, the Hypotenuse is just one, sine and cosine are just Y and X values because if you are trying to divide to find the meaning of sine it would be Y/1 so that would just leave you with Y

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In a unit circle the hypotenuse is always one. when you are looking for sin (opposite over hypotenuse), making it y/1.

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Based on the unit circle the hypotenuse is always going to be one. when looking for the sin or an angle the trig ratio is opposite / hypotenuse . which is considered y/1 because the length opposite to the angle is the height which is measured on the y axis

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Using coordinates of x and y for each trig function, you can create a reference triangle that allows one to see where the points match up to the degrees and radians.

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The x and y are different in the unit circle while the hyp is 1

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The coordinates represent the lengths of the triangle. This is because the hypotenuse is 1. This means that instead of turning into a ratio, sine and cosine just become a number that represents length. Example: Sin=opp/hyp. Because the hypotenuse is 1, sine is equal to the opposite. If the hypotenuse was not 1 then it would become a ratio.

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Within the unit circle hypotenuse is always one no matter where it at, saying that we can tell that cos (X) true when trying to find cosine because it always being divided by one (X/1)

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Because in a unit circle the "hypotenuse" of the triangle will always be one and since sin is opposite over hypotenuse, it would mean sin(Y/1) making it just the y coordinate because the opposite side is the y value for the coordinates