Question

If sin(θ)=−4/7, and θ is in quadrant III, evaluate the following. Leave results as exact values
(a)cos(θ)=
(b) tan(θ)=
(c) sec(θ)=
(d) csc(θ)=
(e) cot(θ)=

Answer 1

Sketch your triangle in quad III, and using your definitions
if sin(θ)=−4/7 , then y = -4, r = 7
x^2 + y^2 = r^2
x^2 + 16 = 49
x^2 = 33
x = -√33, since the angle is in III

Now just use your definitions of the trig ratios,
e.g.
tan(θ) = y/x = -4/-√33 = 4/√33

do the rest in the same way

Answer 2

they want decimal answers