How to Find the Sine of 135 Degrees | Unit Circle Approach and Trigonometric Identities

sin135º

The sine of 135 degrees (sin 135°) can be found using the unit circle or trigonometric identities

The sine of 135 degrees (sin 135°) can be found using the unit circle or trigonometric identities.

Using the unit circle approach:
1. Firstly, draw a unit circle (a circle with a radius of 1 unit).
2. We want to find the sine of 135 degrees, so start from the positive x-axis (0 degrees) and move counterclockwise to the angle 135 degrees.
3. At this angle, draw a vertical line connecting the point on the circle to the x-axis. This line represents the y-coordinate.
4. By definition, the y-coordinate of the point on the unit circle at angle 135 degrees is the sine of 135 degrees.
5. Since the point is in the second quadrant, where the y-coordinate is positive, we can conclude that sin 135° = √2/2 or approximately 0.707.

Using trigonometric identities:
1. There is a common trigonometric identity that links the sine of an angle to the sine of its complementary angle: sin(90° – θ) = cos(θ).
2. In this case, we find that sin(90° – 45°) = cos 45°.
3. Since cos 45° = √2/2 (which can be derived from the unit circle), we conclude that sin 135° = √2/2 or approximately 0.707.

Both methods yield the same answer: sin 135° = √2/2 or approximately 0.707.

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