Answer:
sec θ = -5/3
cot θ = -3/4
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
The point (-3/5,y) in the third quadrant corresponds to angle θ on the unit circle. What is the value of sec θ and the value of cot θ?
My answer:
x -coordinate: -3/5
hypotenuse in this situation is 1 because it is the radius of the unit circle.
As we know:
- sec θ= 1 / cos θ = hypotenuse / x -coordinate
<=> sec θ= 1 / (-3/5) = -5/3
- cot θ = 1 / tan θ = x-coordinate / y - coordinate
<=> cot θ = -3/5 / y
[tex]y^2 + (-3/5)^2 = 1[/tex]
<=> [tex]y^2 = 1 -(-3/5)^2[/tex]
<=> [tex]y^{2} = \frac{16}{25}[/tex]
<=> y = 4/5 or y = -4/5
But The point in the third quadrant => y = 4/5
So cot θ = -3/5 / 4/5 = -3/4
