Final answer:
To find sin 3π/4, locate the angle on the unit circle in the second quadrant, where the sine value, corresponding to the y-coordinate, is √2/2 or about 0.7071.
Step-by-step explanation:
To find sin 3π/4 on the unit circle, consider the angle 3π/4 which is located in the second quadrant of the circle where sine is positive. Since the unit circle has a radius of 1, we can use the trigonometric identities to calculate sine directly.
Recall that the sine of an angle in the unit circle corresponds to the y-coordinate at the point where the terminal side of the angle intersects the unit circle. For angle 3π/4, or 135 degrees, the sine value is √2/2 or approximately 0.7071.Therefore, sin 3π/4 = √2/2.
For anyone learning to calculate the sine of an angle, it's helpful to memorize the unit circle's most common angles and their corresponding sine values.
Additionally, understanding that the unit circle allows you to visualize sine as a y-coordinate can deepen your comprehension of how the sine function works in relation to a circle. Trigonometric identities are also useful tools that can simplify such calculations.