Evaluate the Limit limit as x approaches pi/2 of sin(x)

Problem

(lim_x→π/2)(sin(x))

Solution

1. Identify the type of function. The function ƒ(x)=sin(x) is a trigonometric function that is continuous for all real numbers.

2. Apply the property of continuity for limits. Since the function is continuous at x=π/2 the limit can be found by direct substitution.

3. Substitute the value x=π/2 into the function.

(lim_x→π/2)(sin(x))=sin(π/2)

4. Evaluate the trigonometric value. On the unit circle, the sine of π/2 radians (or 90 is 1

Final Answer

(lim_x→π/2)(sin(x))=1

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