Question

give the exact value of the six trig functions of t=19pi

i know cos t= -1 and sec t= -1 what about the other 4?

Answer 1

19pi is same as pi

sin(pi) = 0
tan(pi) = sin(pi)/cos(pi)

that should help

Answer 2

why si it the same as pi?

Answer 3

because its a cyclical function
sin and cos have periods of 2pi then they repeat values
best example is unit circle, every 2pi radians you go around the circle once and then start again
2pi goes into 19pi nine times ...once you hit 18pi, you restart so essentially all the output values for 19pi are exactly same as pi
this is true for any angle that is an odd numbered factor of pi: 3pi,7pi,25pi , and so on

Answer 4

because a whole circle is 2pi. if we have 19pi that means that we have an extra pi or a pi more to complete another circle. you just have to rewrite all the functions within the pi: following the values of 30, 45, and 60 degrees

Answer 5

check figures at pp 283, 293 and 295 for trigonomic functions

http://finedrafts.com/files/Larson%20PreCal%208th/Larson%20Precal%20CH4.pdf

Answer 6

always write in the format \[2\pi/2\]

Answer 7

so csc and cot are undefined?

Answer 8

depends. they only become undefined if the denominator is zero