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For example you have an equation as such 5sinx-3cosx=1 ..How do you work it out
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Answered by
oobleck
5sinx - 3cosx = 1
5^2+3^2 = 34, so that is the same as
√34 (5/√34 sinx - 3/√34 cosx) = 1
Now, if y is an angle such that tany = 3/5, you have
√34 (cosy sinx - siny cosx) = 1
sin(x-y) = 1/√34
x-y = 9.875°
and, since y = 30.964°, that means
x - 30.964 = 9.875
x = 40.839° or 201.084° + 2kπ
5^2+3^2 = 34, so that is the same as
√34 (5/√34 sinx - 3/√34 cosx) = 1
Now, if y is an angle such that tany = 3/5, you have
√34 (cosy sinx - siny cosx) = 1
sin(x-y) = 1/√34
x-y = 9.875°
and, since y = 30.964°, that means
x - 30.964 = 9.875
x = 40.839° or 201.084° + 2kπ
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