If sin theta = 4/5 and theta is in quadrant 2, the value of cot theta is
2 answers:
Answer:
Cot(theta) = - 0.75 or -3/4
Step-by-step explanation:
The hypotenuse is 5
The y value is 4
We need to find the corresponding x value.
x^2 + y^2 = z^2
X = ?
y = 4
z = 5
x^2 + 4^2 = 5^2
x^2 + 16 = 25
x^2 = 9
Now in this case, you are in quadrant 2, so the x value is - 3
sqrt(x^2) = sqrt(9)
x = - 3
The cot value is the adjacent (x value) / the opposite ( y ) value
Cot(theta) = -3/4
cot(theta) = -0.75
Answer:
cotθ = -3/4
Step-by-step explanation:
<u>Given:</u>
sinθ = 4/5
θ is in Quadrant II, so cosθ < 0
<u>Recall:</u>
cotθ = cosθ/sinθ
cos²θ + sin²θ = 1
<u>Determine cosθ:</u>
cosθ = -√(1-sin²θ) = -√(1-(4/5)²) = -√(1-16/25) = -√(9/25) = -3/5
<u />
<u>Determine cotθ:</u>
cotθ = cosθ/sinθ = (-3/5)/(4/5) = (-3/5)(5/4) = -15/20 = -3/4
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