Question 969721
you have sin(8x) = .97
the period of 8x is equal to 2pi/8.
there will be 8 repetititions of a full sine wave sycle in a standard 0 to 2pi interval.


use your calculator to find that sin(8x) = .97 leads to an angle of 8x = 1.325230809.


since sine is positive in the first and second quadrant, than you need to get the angle in the second quadrant as well.


that angle sill be pi - 1.325230809 = 1.816361844.


those angles are 8x.


you want angles of x.


divide those angles by 8 and you will get:


x1 = .1656538512
x2 = .2270452305


those angles will repeat every full cycle of 2pi/8.


your solution is therefore equal to:


x1 = .1656538512 plus or minus k * 2pi/8.
x2 = .2270452305 plus or minus k * 2pi/8.


your smallest angle in the interval from 0 to 2pi will be x1 = .1656538512.


your largest angle in the interval from 0 to 2pi will be x2 = .2270452305 + 7*2pi/8 = 5.724832374.


the graph below shows the function of y = sin(8x) in the interval from 0 to 2pi.
the smallest value of x and the largest value of x where sin(x) = .97 are marked.


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