The point given below is on the terminal side of an angle theta in standard position. Find the exact value of each of the six trigonometric functions of theta. The point is (-5,12).

Answer 1

The point is in the 2nd quadrant. The sine and csc are positive; the other 4 functions are negative.

The distance from the origin to the point is 13 (this is a 5, 12, 13 right triangle...Pythagorean Theorem).

With this information you should be able to use the definition of the trig functions to answer the question.

Answer 2

(-5,12) = (x,y)

hypotenuse = sqr(x^2 +y^2) = sqr(25+144) = sqr169=

13=h

cosT = x/h =-5/13

secT = h/x = -13/5= -2.6

sinT = y/h = 12/13

cscT =x/y = -13/12

tanT = y/x = 12/-5 =- 2.4

cotT = -5/12