is it possible to find sin tan and cos of a right angle?

Question

lets say theres a right triangle. i know all the formulas, but if you're trying to find sin tan and cos for the right angle, then which side is opposite and which side is adjacent? or is this even possible?

none of the answers i think understand my question.. what i'm saying is that you know how sin is opposite/hypotenuse, cos is adjacent/hypotenuse and tan is opposite/adjacent.. well picture a right triangle. how do you know which side is opposite or adjacent to the right angle?

Answer 1

sin 90 = 1

cos 90 = 0

tan 90 = sin / cos = undefined

You would only use this using the law of sines where c/sinC = a/sinA = b/sinB

Answer 2

sin 90 = 1
cos 90 = 0
tan 90 is undefined
We do refer to the side adjacent when referring to the right angle. The side opposite the right angle is the hypotneuse. The other two sides are called the legs of the right triangle.

When x= 90 degrees the hypotenus becomes equal to the longer leg and so sin 90 =1/hypotenuse = 1

When x = 90 degrees the shorter leg becomes zero so cos 90 = 0/hypotenuse = 0.

When x = 90 degrees the tan = loger leg / 0 which is undefined.

Answer 3

Consider the 89 deg angle in a triangle with angles 90 deg, 89 deg, 1 deg, and the side opposite the 1 deg angle = 1 unit in length.
sin 89 deg is almost 1.
cos 89 deg is almost 0.
tan 89 deg is extremely large.
As you increase the 89 deg angle towards 90 deg, the sin gets even closer to 1, the cos even closer to 0, and the tan even larger.
This is an informal explanation of what is known in maths as limiting values. The limiting values are what we consider to be the ratios you require for 90 deg.
This is not a formal proof, but just an insight into how the generally accepted values of these ratios are 1 for the sin, 0 for the cos, and infinity for the tan.

Answer 4

sin, tan and cos for any angle is defined based on the triangle shaped by the x and y coordinates associated with a line tilted at the appopriate angle is equal to length 1.

Thus any angle for which sin, tan and cos are being calculated is based on the x and y associated with that angle.

i.e. 45 degree line drawn out to length 1 has an "x" and a "y" equal to the (square root of 2) divided by 2.

sin = y/1
cos = x/1
tan = sin/cos or y/x

for a 90 degree angle this triangle looks like a straight line straight up, or x = 0, y = 1

thus

sin (90) = 1/1 or 1
cos (90) = 0/1 or 0
tan (90) = 1/0 or undefined

Answer 5

change the definition for determining sin and cos

the right angle triangle with opposite and adjacent side is good for 30 ,45, 60 etc degree angles

Sine and cosine 'original' definition is the projections on the x and y axis of a point traveling along the unit circle with a center at (0,0) Cosine is the x projection, sine -- y. The angle is 0 when the point is at (1,0) and increases counter clockwise

So when the point is at (1,0) you have cos0 =1 sin0 =0
when the point is up at (0,1) you have cos90=0 sin90=1

see, no problems here

tan = sin / cos

so tan0=0 and tan90=infinity

Answer 6

30-60-90 Triangle

View opposite from the 30° vertex is the opposite side

View oopposite from the 60° vertex is the adjacent side

The side oppposite tht 90° angle is the hypotenuse

www.mathopenref.com/triangle306090.html

- - - - - - - - - - s-

Answer 7

extra suggestions is given. The ratio, sin (a) / cos(a) = tan (a). Sine is damaging and cosine is advantageous, ensuing in tangent being damaging. If we consult with a unit circle , a circle of radius a million, sine is the size interior the up/down (or y) path and cosine is the size interior the left/spectacular (or x) path. A unit circle is split into 4 quadrants: 0 to ninety, ninety to one hundred eighty, one hundred eighty to 270, and 270 to 360. the place is cosine advantageous? To the excellent suited (+) of the vertical axis: 0 to ninety, 270 to 360 the place is sine damaging? below (-) the horizontal axis: one hundred eighty to 360 the respond, a could be placed the place the two coincide: 270 to 360. a available answer for a could be a = 290 tiers.

Answer 8

You'll find it's a right angled triangle with no height and infinite length.

Answer 9

YOu cannot get the tan of 90 deg!