Question

attachment derivate of sinx​

Answer 1

Answer:

I'm trying to show that the derivative of sinθ is equal to π/180cosθ if θ is measured in degrees. The main idea is that we need to convert θ to radians to be able to apply the identity d/dxsinx=cosx.

Answer 2

Answer:

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=1limit, start subscript, x, \to, 0, end subscript, start fraction, sine, left parenthesis, x, right parenthesis, divided by, x, end fraction, equals, 1

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x

1−cos(x)

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=0limit, start subscript, x, \to, 0, end subscript, start fraction, 1, minus, cosine, left parenthesis, x, right parenthesis, divided by, x, end fraction, equals, 0

Now we are ready to prove that the derivative of \sin(x)sin(x)sine, left parenthesis, x, right parenthesis is \cos(x)cos(x)cosine, left parenthesis, x, right parenthesis.

Finally, we can use the fact that the derivative of \sin(x)sin(x)sine, left parenthesis, x, right parenthesis is \cos(x)cos(x)cosine, left parenthesis, x, right parenthesis to show that the derivative of \cos(x)cos(x)cosine, left parenthesis, x, right parenthesis is -\sin(x)−sin(x)minus, sine, left parenthesis, x, right parenthesis.

Explanation: