if sinA=-(12/13) and -90<A<0, find without using calcuator, the value of cot(90-A)

2 answers

cot(90-A)= -2.40 approximately
use arcsinA or 1/sinA =-(12/13) to get the value of A..or use sine graph..to get the answer.
cotangent=cosx/sinx..
just input the value of A which is -67.38 to that of formula above with x as (90-A)...
It said "without a calculator"
All the work following is done in my head.

sinA = -12/13 = y/r
x^2 + y^2 = r^2
x^2 + (-12)^2 = 13^2
x^2 + 144 = 169
x^2 = 25
x = ± 5 , but A is in quad IV, so x = 5

so sinA = -12/13, cosA = +5/13
tanA = (-12/13) / (5/13) = -12/5

since cot(90-A) = tanA
cot(90-A) = -12/5 = -2.4
(exactly, not approximately)