# sine, cosine, tangent?

Find the sine, cosine, and tangent ratios for Angle X and Angle Y. This triangle is a right triangle. The hypotenuse (XY) is 13 in length, the base (XZ) is 12 in length, and the leg (YZ) is 5 in length.

i have no idea. anyone know? =[

Relevance

Remember this mnemonic:

"Some People Have, Curly Brown Hair, Turned Permanently Black" (Where S = Sine, P = Perpendicular(adjacent), H = Hypotenuse, C = Cos , B = base, T = Tan.)

For the triangle given, this is:

Sine = 5/13

Cosine = 12/13

Tangent = 5/12

• The sine of any angle is defined as the opposite (the side measurement of either base or leg directly across from the angle) divided by the hypotenuse.

The cosine of any angle is defined to be the adjacent (the side [base or leg] that helps to form the angle in question) divided by the hypotenuse.

The tangent of any angle is defined to be the opposite divided by the adjacent.

With this known, the answers are as follows:

For angle X:

sin x = 5/13

cos x = 12/13

tan x = 5/12

Whereas angle Y:

sin y = 12/13

cos y = 5/13

tan y = 12/5

I hope this solves your problem and good luck!!

• Since the hypotenuse is XY, let's assume the X is the top angle and Y is the bottom angle of the hypotenuse.

Remember SOHCAHTOA.

To find angle X, all we have to do is apply one of the above three formulas. Let's use sin

sin(X) = opp/hyp

The "opposite" of X is the side which angle X projects on; since angle X was given to be the top of the triangle, it projects on the base. Therefore, opp=XZ = 12. Hypotenuse is given to be 13.

Therefore, sin(X) = 12/13.

To solve for X, take the sin inverse of both sides, using your calculator. On most scientific calculator, it's 2nd function sin.

X = sin^(-1)(12/13)

Whatever value you get for that will be your angle. Also make sure that your calculator is in DEG (degree mode).

To solve for angle Y (i.e. the bottom angle that isn't the right angle), do the same thing. since we're given all the sides, we can choose sin, cos, OR tan. Let's try tan instead.

The "opposite" in this case would be the leg of the triangle, YZ, which is 5. The adjacent is usually the remaining side that is neither the opposite nor hypotenuse. Therefore, it's the base, 12.

tan(Y) = 5/12, therefore

Y = tan^(-1)[5/12]

Since you were asking for the ratios, however:

sin(X) = opp/hyp = 12/13

sin(Y) = 5/13

cos(Y) = 12/13

tan(Y) = 5/12

• You need to remember the mythical indian chief of trigonometry. His name is SOHCAHTOA. Basically, this means sine = opposite/hypoteneuse, cosine = adjacent/hypoteneuse, and tangent = opposite/adjacent. So, in your example sin X = 5/13, cos X = 12/13, and tan X = 5/12. Try it on your own with Y. You might find that drawing a picture of the triangle will be helpful in determining which sides are adjacent or opposite of a given angle.

• Sin theta = Opp/Hyp; cos theta = adj/hyp; tan theta = opp/adj;

These three ratios are important in trigonametry. Now coming to your problem, sides xz = 12; zy = 5; and xy = 13. With the ratios given above, we get sin x = 5/13; cos x = 12/13; and tan x = 5/12.

sin y = 12/13; cos y = 5/13; and tan y = 12/5. I hope this is clear to you. You can contact me anytime if you have doubt.

For angle x, zy is the opposite side and xz is the adjacent side.

For angle y, xz is the opposite side and zy is the adjacent side. Draw a triangle and see for yourself.

• sine X = 5/13

cosine X = 12/13

tangent X = 5/12

sine Y = 12/13

cosine Y = 5/13

tangent Y = 12/5

• sine = 5/13

cosine = 12/13

tangent = sine/cosine = (5/13) / (12/13) = 5/12

• Anonymous

Angle Z = 90

Angle X = inverse sin (5 / 13) = 22.62

Angle Y = 90 - 22.62 = 67.98

tan(90) = Undefined

cos(90) = 0

sin(90) = 1

tan(22.62) ~ 0.4166694329897247697169290965586

cos(22.62) ~ 0.92307601649691425248484768326348

sin(22.62) ~ 0.38461756040018308919419477510733

tan(67.98) ~ 2.4726015381241626899834710560552

cos(67.98) ~ 0.37493021880767134457175525452862

sin(67.98) ~ 0.92705303571307703730990185991509

• Anonymous