The given point (-3/5 , y) lies in the third quadrant.
It is also given that the point lies on a unit circle.
For a point (x,y) lying on a unit circle a and y are defined as:
x = cos θ
y = sin θ
So, we can say for the point (-3/5 , y) the value -3/5 is equal to cos θ
sec θ is the reciprocal of cos θ.
So, sec θ = -5/3
[tex]cot\theta= \frac{cos\theta}{sin\theta} [/tex]
Using Pythagorean identity we can first find sin θ.
[tex]sin \theta = - \sqrt{1- cos^{2}\theta } \\ \\
sin\theta= \sqrt{1-( -\frac{3}{5})^{2} }=- \frac{4}{5} [/tex]
Since the point lies in 3rd quadrant, both sin and cos will be negative.
So, now we can write:
[tex]cot\theta= \frac{ \frac{-3}{5} }{ \frac{-4}{5} } \\ \\
cot\theta= \frac{3}{4} [/tex]
Answers:
sec θ = -5/3
cot θ = 3/4
