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D\'eterminer deux angles entre 00^\circ et 360360^\circ qui ont une cos\'ecante de 55

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Q. D\'eterminer deux angles entre 00^\circ et 360360^\circ qui ont une cos\'ecante de 55
  1. Find Sine of Angle: Cosecant is the reciprocal of sine, so we need to find the sine of an angle that is 15\frac{1}{5}. \newlinesin(θ)=1csc(θ)=15\sin(\theta) = \frac{1}{\csc(\theta)} = \frac{1}{5}
  2. Calculate Angle: Now we find the angle whose sine is 15\frac{1}{5}. We use a calculator or inverse sine function.\newlineθ=sin1(15)\theta = \sin^{-1}(\frac{1}{5})
  3. Calculate First Angle: Calculating the angle gives us:\newlineθ11.54\theta \approx 11.54^\circ\newlineThis is the first angle in the first quadrant.
  4. Find Second Angle: Since sine is positive in the first and second quadrants, we need to find the second angle in the second quadrant.\newlineThe second angle will be 180°θ180° - \theta.
  5. Calculate Second Angle: Calculating the second angle: 18011.54168.46180^\circ - 11.54^\circ \approx 168.46^\circ This is the second angle in the second quadrant.

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