The point 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?

sec θ = -5/3

cot θ = -3/4

Step-by-step explanation:

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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

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 / (-3/5) = -5/3

<=> cot θ = -3/5 / y

<=>

<=>

<=> 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

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< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

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