
Steve S. answered 01/01/14
Tutor
5
(3)
Tutoring in Precalculus, Trig, and Differential Calculus
tan(x) = 4/11, sec(x) < 0
tan > 0 in quadrants I & III.
sec(x) = 1/cos(x) < 0 in II & III
So x lies in quadrant III:
............ -4
..... _______
..... | ........../
..... | ........ /
..... | ....... /
..... | ...... /
..... | ..... / sqrt(137)
-11 | ...../
..... | .../
..... | ../
..... | ./
..... | /
..... |/
sin(x) = -11/sqrt(137)
cos(x) = -4/sqrt(137)
tan(x) = sin(x)/cos(x) = -11/(-4) = 11/4
cot(x) = 1/tan(x) = 4/11
sec(x) = 1/cos(x) = -sqrt(137)/4
csc(x) = 1/sin(x) = -sqrt(137)/11
tan > 0 in quadrants I & III.
sec(x) = 1/cos(x) < 0 in II & III
So x lies in quadrant III:
............ -4
..... _______
..... | ........../
..... | ........ /
..... | ....... /
..... | ...... /
..... | ..... / sqrt(137)
-11 | ...../
..... | .../
..... | ../
..... | ./
..... | /
..... |/
sin(x) = -11/sqrt(137)
cos(x) = -4/sqrt(137)
tan(x) = sin(x)/cos(x) = -11/(-4) = 11/4
cot(x) = 1/tan(x) = 4/11
sec(x) = 1/cos(x) = -sqrt(137)/4
csc(x) = 1/sin(x) = -sqrt(137)/11