Whats the derivative of sin^2(theta)?

Thread starter M. next
Start date May 10, 2012
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Derivative

In summary, the derivative of sin^2(theta) is 2sin(theta)cos(theta). To find the derivative of sin^2(theta), you can use the chain rule and the derivative of sin(theta) which is cos(theta). The derivative of sin^2(theta) is useful in finding the slope or rate of change of a function that involves sin^2(theta). No, the derivative of sin^2(theta) is not the same as the derivative of cos^2(theta). The derivative of sin^2(theta) can be simplified to sin(2theta).

May 10, 2012

M. next

but i need the derivative wrt time where theta depends on time

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May 10, 2012

Mark44

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M. next said:

but i need the derivative wrt time where theta depends on time

Use the chain rule.
$$\frac{d}{dt}sin^2(\theta) = \frac{d}{d\theta}sin^2(\theta)\cdot \frac{d\theta}{dt} = ? $$

May 10, 2012

M. next

then it is simply 2sin(theta)cos(theta)*(theta dot)

May 11, 2012

Mark44

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Yes, that's it.

What is the derivative of sin^2(theta)?

The derivative of sin^2(theta) is 2sin(theta)cos(theta).

How do you find the derivative of sin^2(theta)?

To find the derivative of sin^2(theta), you can use the power rule and the chain rule. First, rewrite the function as (sin(theta))^2, then apply the power rule to get 2sin(theta). Finally, multiply by the derivative of the inner function, which is cos(theta), to get 2sin(theta)cos(theta).

What is the general rule for finding the derivative of a trigonometric function raised to a power?

The general rule for finding the derivative of a trigonometric function raised to a power is to use the power rule and the chain rule. Rewrite the function as (trig function)^n, then apply the power rule to get n(trig function)^(n-1). Finally, multiply by the derivative of the inner function to get the final answer.

Can the derivative of sin^2(theta) be simplified further?

Yes, the derivative of sin^2(theta) can be simplified further as sin(2theta). This is a trigonometric identity that can be derived using the double angle formula for sine.

What is the significance of the derivative of sin^2(theta)?

The derivative of sin^2(theta) represents the rate of change of the function at any given point. It is also used in various applications such as in physics and engineering to calculate velocities and accelerations of objects in circular motion.