We can find the solutions of \sin x = 0.3 algebraically. First we find the solutions in the interval [0, 2 \pi). We get one such solution by taking \sin^{-1} to get x\approx______. We find all solutions by adding multiples of _____ to the solutions if [0, 2 \pi).

nicekikah 2021-08-06 Answered
We can find the solutions of sinx=0.3 algebraically.
a) First we find the solutions in the interval [0,2π). We get one such solution by taking sin1 to get x______. The other solution in this interval is x______.
b) We find all solutions by adding multiples of _____ to the solutions if [0,2π). The solutions are x_______ and x_______.
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Expert Answer

smallq9
Answered 2021-08-07 Author has 106 answers
To determine
a)
To complete:
The statement "First we find the solutions in the interval [0,2π). We get one such solution by taking 7sin1 to
get x ______. The other solution in this interval is x ______.
Approach:
The range of the trigonometry function of sinθ is lies between [1,1]. No solution exists beyond this range. Sine has period 2π, we find solution in any interval of length 2π. Sine function is positive in first and second quadrant.
Calculation:
Consider the trigonometry equation.
sinθ=0.3..(1)
Multiply sin1 both side in equation (1).
sin1(sinθ)=sin1(0.3)
θ10.30
θ22.83
Therefore, the appropriate answers are θ10.30 and θ22.83.
Conclusion:
Thus, the appropriate answers are θ10.30 and θ22.83.
b) We find all solutions by adding multiples of _____ to the solutions if [0,2π). The solutions are x_______ and x_______.
Approach:
Sine has period 2π, we find solution in any interval of length 2π. Sine function is positive in first and second quadrant.
The function repeats its value every 2π units, so we get all solutions of the equation by adding integer multiples of 2π to these solutions.
Calculation:
Consider the solutions.
θ0.30
θ2.83
The function repeats its value every 2π units. So we get all solutions of the equation by adding integer multiples pf 2π to these solutions.
θ30.30+2kπ
θ32.83+2kπ
Therefore, the appropriate answers are 2π,θ30.30+2kπ and θ42.83+2kπ
Conclusion:
Thus, the appropriate answers are 2π,θ30.30+2kπ and θ42.83+2kπ
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