what is the relationship between sin of thata and cos of thata at every ten degrees?
To understand the relationship between the sine (sin) and cosine (cos) of an angle theta (θ) at every ten degrees, we can refer to the unit circle. The unit circle is a circle centered at the origin with a radius of 1.
To find the sin and cos values at specific angles, we need to determine the coordinates where the terminal side of the angle intersects the unit circle.
For each angle θ, we can use the following steps to find the sin and cos values:
1. Convert the angle to radians: Multiply the degree measure by π/180 to convert it to radians since trigonometric functions typically operate in radians.
2. Identify the point of intersection on the unit circle: In the unit circle, look for the coordinates where the terminal side of the angle intersects with the circle. The x-coordinate represents the cos(θ), and the y-coordinate represents the sin(θ).
Now, let's consider the angles at every ten degrees starting from 0°:
- 0°: The point of intersection on the unit circle is (1, 0), which means cos(0°) = 1 and sin(0°) = 0.
- 10°: The point of intersection on the unit circle is approximately (0.9848, 0.1736). Therefore, cos(10°) ≈ 0.9848 and sin(10°) ≈ 0.1736.
- 20°: The point of intersection on the unit circle is approximately (0.9397, 0.3420). Therefore, cos(20°) ≈ 0.9397 and sin(20°) ≈ 0.3420.
- Continue this process for 30°, 40°, 50°, 60°, 70°, 80°, 90°, and so on, until you have calculated the sin and cos values for each angle.
By repeating these steps for each angle at every ten degrees, you will be able to determine the relationship between sin(θ) and cos(θ) at those angles.