how to solve for the value of sine and cosine function of 0,90,180 and 270 degrees?
best way is to memorize and sketch the curves of both the sine and cosines curves, marking in those critical 4 values.
After 55 years of doing this, I still sketch them .
To solve for the values of the sine and cosine functions at 0, 90, 180, and 270 degrees, you can use the unit circle.
Here are the steps to find the values:
1. Start with the unit circle, which is a circle with a radius of 1.
2. Label the angles 0, 90, 180, and 270 degrees on the circle.
3. For each angle, find the coordinates of the point where the angle intersects the circle.
- At 0 degrees, the point is (1, 0).
- At 90 degrees, the point is (0, 1).
- At 180 degrees, the point is (-1, 0).
- At 270 degrees, the point is (0, -1).
4. The x-coordinate of each point represents the cosine value, while the y-coordinate represents the sine value.
- At 0 degrees, cosine is 1 and sine is 0.
- At 90 degrees, cosine is 0 and sine is 1.
- At 180 degrees, cosine is -1 and sine is 0.
- At 270 degrees, cosine is 0 and sine is -1.
So, the values of the sine and cosine functions at 0, 90, 180, and 270 degrees are:
- Sine: 0, 1, 0, -1
- Cosine: 1, 0, -1, 0
To solve for the values of sine and cosine functions at standard angles (0°, 90°, 180°, and 270°), you can use the unit circle or reference triangles. Here's how:
1. Sine Function (sin):
- Start with the unit circle: draw a circle with a radius of 1 unit.
- For 0°, the coordinates on the unit circle are (1, 0). Therefore, sin(0°) = 0.
- For 90°, the coordinates are (0, 1). Hence, sin(90°) = 1.
- For 180°, the coordinates are (-1, 0). Hence, sin(180°) = 0.
- For 270°, the coordinates are (0, -1). Therefore, sin(270°) = -1.
2. Cosine Function (cos):
- Again, refer to the unit circle.
- For 0°, the coordinates are (1, 0). Hence, cos(0°) = 1.
- For 90°, the coordinates are (0, 1). Therefore, cos(90°) = 0.
- For 180°, the coordinates are (-1, 0). Hence, cos(180°) = -1.
- For 270°, the coordinates are (0, -1). Hence, cos(270°) = 0.
Remember, these values are specific to the standard angles and can be used as reference points when dealing with more complex angles.