Find the exact value of csc ø, if cos ø= 1/9; 180° less ø less than 270°
1 answer:
Answer:
The answer to your question is: the first option - 9/
Step-by-step explanation:
Process
cosФ = adjacent side / hypotenuse
-1/9 = adjacent side / hypotenuse
adjacent side = -1 hypotenuse = 9
c² = a² + b²
b² = c² - a²
b² = 81 - 1
b = b = opposite side
But b is negative because we are in the third quadrant.
b = -
Finally csc Ф = hypotenuse / opposite side
csc Ф = - 9 /
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by separating the variables
∴ y dy = -x dx
integrating both sides with respect to x
∴ ∫y dy = ∫-x dx
∴
finding c using initial condition y(2) = 2.
∴
∴ c = 4
∴
multiplying all the equation by 2
∴ y² = -x² + 8
∴ x² + y² = 8
The resultant equation represents the equation of the circle
with center (0,0) and radius = √8 = 2√2
so, the domain of this function is [-2√2 , 2√2]
See the attached figure
