Question

The point (-3/5,y)in the third quadrant corresponds to angle θ on the unit circle.

Answer 1

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

$cot\theta= \frac{cos\theta}{sin\theta}$

Using Pythagorean identity we can first find sin θ.

$sin \theta = - \sqrt{1- cos^{2}\theta } \\ \\ sin\theta= \sqrt{1-( -\frac{3}{5})^{2} }=- \frac{4}{5}$

Since the point lies in 3rd quadrant, both sin and cos will be negative.

So, now we can write:

$cot\theta= \frac{ \frac{-3}{5} }{ \frac{-4}{5} } \\ \\ cot\theta= \frac{3}{4}$

Answers:
sec θ = -5/3
cot θ = 3/4

Answer 2

Hello,

cos(x)=-3/5

sin(x)=-√(1²-(-3/5)²=-4/5

sec(x)=1/ cos(x)=1/-(3/8)=-5/3

cot(x)= cos(x)/sin(x)=(-3/5)/(-4/5)=3/4