Question

Как из cos(2*10π+π+) получить cos(π+π/2+) ?

Answer 1

В силу периодичности косинуса (его период равен 2пи) мы можем упростить выражение cos(2*10π+π+ ).
Так как 2*10π=10*2π, то  cos(2*10π+π+ ) =cos(π+9π/18+)=
=cos(π+π/2+)

Используя формулы приведения можно упростить и дальше:

=cos(3π/2+2π/9)=sin(2π/9)

Answer 2

Transformation of cos(2*10π+π+) to cos(π+π/2+)

To transform the expression cos(2*10π+π+) to cos(π+π/2+), we can simplify the given expression and then apply trigonometric identities to obtain the desired form.

First, let's simplify the given expression: cos(2*10π+π+)

Using the property that cos(x+2π) = cos(x), we can simplify the expression as follows: cos(2*10π+π+) = cos(2*10π+π+2π)

Now, we can apply the trigonometric identity cos(x+π) = -cos(x) to further simplify the expression: cos(2*10π+π+2π) = -cos(2*10π)

Finally, we can use the property that cos(x+π/2) = -sin(x) to transform the expression into the desired form: cos(π+π/2+) = -sin(2*10π) = -sin(20π)

So, the transformation of cos(2*10π+π+) to cos(π+π/2+) results in -sin(20π).

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