Find the Value Using the Unit Circle sin(-1)

Problem

sin(−1)

Solution

1. Identify the input of the function. The expression sin(−1) refers to the sine of −1 radian, as there is no degree symbol.

2. Understand the unit circle definition. On a unit circle, sin(θ) represents the ycoordinate of a point after rotating θ radians from the positive xaxis.

3. Determine the direction of rotation. A negative angle indicates a clockwise rotation from the positive xaxis.

4. Evaluate the value. Since −1 radian is not one of the standard "special" angles (like π/6 or π/4, the value is typically expressed as the function itself or approximated using a calculator.

5. Apply the odd function property. The sine function is odd, meaning sin(−x)=−sin(x) Therefore, sin(−1)=−sin(1)

Final Answer

sin(−1)=−sin(1)

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