Question

Find the value of the six trigonometric functions of 0, where 0 angle formed by positive x-axis and line segment from (0,0)to(-5,-4).

Sin(0)=_________
cos(0)=_________
tan(0)=_________
sec(0)=_________
csc(0)=_________
cot(0)=_________

Answer 1

The hypotenuse of the trig functions for the point -5,-4 = sqrt( (-5)^2 + (-4)^2 )

is sqrt(25 + 16) = sqrt(41)

So Sin(∅)  = y value / hypotenuse = -4/sqrt(41) = -4sqrt(41)/41

Cos(∅) = x value / hypotenuse = - 5/ sqrt(41) = -5 sqrt(41)/41

Tan(∅) = y value / x value = - 4 / - 5 = 4/5

Sec(∅) = hypotenuse / x value  = sqrt(41) / - 5

Csc(∅) = hypotenuse / y value = sqrt(41) / - 4

cot(∅) = adjacent / opposite = x value / y value = - 5/-4 = 5/4 = 1.25