Let’s take an example

####
**
If cos x = –12/13 lies in second quadrant, find value of
**
**
other five trigonometric
**
**
functions
**

Since x is in 2nd Quadrant,

tan and cos will be negative

But sin will be positive

Given cos x = –12/13

We know that

sin
^{
2
}
x + cos
^{
2
}
x = 1

sin
^{
2
}
x + (-12/13)
^{
2
}
= 1

sin
^{
2
}
x + 144/169 = 1

sin
^{
2
}
x = 1 – 144/169

sin
^{
2
}
x = (169 – 144)/169

sin
^{
2
}
x = 25/169

sin x = ±√(25/169)

sin x = ±√25 / √169

sin x = ± 5/13

Since, x is in 2nd Quadrant

sin x is positive

∴ sin x = 5/13