Find cos theta and cot theta if sin =1/4 and tan theta <0

Answer 1

make a sketch of a triangle in quadrant II, with opposite side 1 and hypotenuse 4
y = 1, r = 4, x = ?
x^2 + 1^2 = 4^2
x = ±√15 , but we know that the angle must be in quadrant II since the sine is positive and the tangent is negative only in quadrant II
so x = -√15

cos theta = -√15/4,
tan thetat = 1/-√15 so cot theta = -√15