Final answer:
The exact value of sin π/6 is 0.5, which can be determined from the unit circle and by considering a 30-60-90 triangle. This value is reasonable as it falls within the expected range of sine values for angles between 0 and π/2.
Step-by-step explanation:
The student has asked to find the value of sin π/6. This is a well-known value in trigonometry, and we can find the exact value without the use of a calculator. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
From the unit circle, we know that sin π/6 is equal to 1/2. This is because π/6 radians corresponds to 30 degrees, and in an equilateral triangle split down the middle into two 30-60-90 right triangles, the side opposite the 30-degree angle (π/6 radians) is half the hypotenuse. Therefore, the exact value of sin π/6 is 0.5.
To check if the answer is reasonable, we can consider that sine values range from -1 to 1 and that sine values for angles between 0 and π/2 (0 and 90 degrees) are positive. Since π/6 is in this range, a positive result less than 1 is expected, which is the case for 0.5.