Determine the solutions to the equation #cosx//sin2x=5/7# for #0lexle2pi# accurate to two decimal places?

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Answer 1 · 2018-04-14T04:45:50

#arcsin(7/10)approx0.78, pi - arcsin(7/10) approx 2.37#

Recall that #sin2x=2sinxcosx#. We then have

#cancelcosx/(2sinxcancelcosx)=5/7#

#1/sinx=10/7#

Flip both sides:

#sinx=7/10#

Using a calculator (with measures set to radians), the answer accurate to two decimal places is

#arcsin(7/10)approx0.78#

Accounting for the periodic nature of the sine function,

#π−arcsin(0.7)≈2.37 # should also be included,