why does a 270-degree angle have following trig values: sin=-1, cos=0, tan=undefined?

Question

why does a 270-degree angle have following trig values: sin=-1, cos=0, tan=undefined? can anyone ex this to me please?plain

Answer 1

Imagine a point rotating around a circle with a radius of 1. The point starts at an angle of 0 degrees, so it's at (1,0). Watch the x and y coordinates as the angle rotates.



270 degrees is 3/4 the way around the circle, so the x coordinate (cosine) is at 0, the y coordinate (sine) is at -1, and the tangent (y/x) is at -1/0 which is undefined!

Answer 2

Start with a 240 degree angle. Draw a vector from the origin to the point the angle is at, and another one from the point to the x-axis. The reference angle of 240 is whatever it is. You drew a triangle with the vectors, and it would be easy to find any side of that triangle using the Pythagorean theroem or the trig identities tan x = opp/adj, etc. You cant exactly do that with a 270 degree angle, or even a 90, 180, and 360, because one of the vectors would be missing. You also have to remember that sin, cos, and tan are just ratios, not numbers.

Answer 3

ok 180* is 1 pie( the greek letter) so 270 is 3pie/2 or 1 1/2 pie



on the unit circle the coordinates of 270 would be (0,-1)

sint= y

so sint=-1



cost =x

so cos= 0



tant= sin/cos

so tan= -1/0

any number over 0 means the number is undefined but if the 0 is over the number then it is 0.

Answer 4

Everything comes from a 360 degree circle. The circle is broken up into four quadrants. In each of the quadrants the Mathematical sign changes. If I could draw you a picture here, I could explain it to you very easily. If you really need it, you can write to me and I will send you a full explanation.



Sin = X/Z Cos = R/Z AND Tan = X/R Those are Electronic symbols.



Z is the hypotenuse of a right triangle

R is the adjacent side to the angle

X is the opposite side of the angle.

Answer 5

'cause :



tan = sin/cos



tan(270) = sin(270) / cos(270) = -1 / 0 = -oo



oo = infinity



it's the same for 90° 'cause cos(90) = 0

Answer 6

Two words: UNIT CIRCLE. The easiest way to learn trig is to understand the Unit Circle. Try here:



http://www.ncsu.edu/felder-public/kenny/papers/trig.html