Discover The Limit Of Sin(Theta)/Theta As Theta Approaches Zero With A Trigonometric Identity

limit of theta goes to zero of sin(0)/0=?

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The expression sin(0)/0 is undefined because division by zero is not allowed in mathematics. Therefore, it is not possible to directly evaluate the limit of this expression as theta approaches zero.

However, we can use a trigonometric identity to rewrite the expression into a form that can be evaluated. Specifically, we can use the identity:

lim x->0 (sin x)/x = 1

This identity tells us that as x approaches 0, the ratio of sine x to x approaches 1.

Therefore, if we rewrite sin(0)/0 as sin(theta)/theta and apply the above identity, we can evaluate the limit as:

lim theta->0 (sin(theta)/theta)
= 1

So, the limit of sin(theta)/theta as theta approaches zero is equal to 1.

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