If sin θ= 4/5 and theta is in quadrant 2, the cot θ would be -3/4.
Which trigonometric functions are positive in which quadrant?
In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
In second quadrant(π/2 < θ < π), only sin and cosec are positive.
In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.
Given information; If sin θ= 4/5 and theta is in quadrant 2, we need to find the value of cot theta.
Since it’s in second quadrant, cos is going to be negative.
So, a^2 + 4^2 = 5^2
a^2 + 16 = 25
a^2 = 25 - 16 = 9
a = 3
therefore, we can conclude that cos θ = base / hypotenuse
cos θ =-3/5
Also, tan θ would be -4/3 and then cot θ would be -3/4.
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