Find the approximate value of cot θ, given that csc θequals=3.5891420 and θ is in quadrant I.
cot = 1/tan = cos/sin
csc = 1/sin
so
cot = csc*cos
cos = sqrt(1-sin^2)
cot = 3.589142*sqrt(1-1/3.589142^2)
=3.447019
or
3.45
thank you!
csc^2 θ = 1+cot^2 θ
so, ...
To find the approximate value of cot θ, we need to first find the value of sin θ since csc θ is given.
Given that csc θ = 3.5891420, we can find sin θ using the reciprocal relationship between csc and sin:
sin θ = 1 / csc θ
sin θ = 1 / 3.5891420
Now, we can find the value of cot θ using the reciprocal relationship between cot and sin:
cot θ = 1 / tan θ
Since θ is in quadrant I, sin θ is positive. Therefore, we can find the value of cos θ using the Pythagorean Identity:
cos θ = sqrt(1 - sin^2 θ)
To find tan θ, we can use the relationship between tan and sin:
tan θ = sin θ / cos θ
Finally, we can find the approximate value of cot θ using the reciprocal relationship:
cot θ = 1 / tan θ
Using these steps, we can find the value of cot θ.