Why do we take sin on Y axis and COS x-axis?

So z = sin(θ) which means that the length of the line between the x-axis and the point on the circle is sin(θ). This is why the y-axis is called the “sine” – that’s what it represents on a triangle.

Why does sin correspond to the Y coordinate?

According to the definition of sinθ it is the ratio of the side opposite of the angle to the hypotenuse of the triangle. BC is parallel to Y-axis so we take the lengths parallel to Y-axis in terms of sinθ. Similarly, cosθ definition is the ratio of the side adjacent to the angle and the hypotenuse.

Why is the sine value the Y coordinate on the unit circle?

Because the sine value is the y-coordinate on the unit circle, the other angle with the same sine will share the same y-value, but have the opposite x-value. Therefore, its cosine value will be the opposite of the first angle’s cosine value.

Is X component sin or cos?

If the angle is the angle between the eastern axis and the vector, then the leg adjacent the angle is the x-component and the leg opposite the angle is the y-component. Thus, the cosine function is used to calculate the x-component and the sine function is used to calculate the y-component.

Is the Y component always sin?

x-comp) and sin will always give the y-comp. because in this case all angles are given relative to the +ve x-axis (going clockwise), you don’t have to worry about anything at all.

At what point are sine and cosine the same value?

First, we will look at angles of 45° or π4, as shown in Figure 2.1. 9. A 45°–45°–90° triangle is an isosceles triangle, so the x- and y-coordinates of the corresponding point on the circle are the same. Because the x- and y-values are the same, the sine and cosine values will also be equal.

Are sin and cos equal?

You just verified the Complementary Angle Theorem: The sine of an angle is equal to the cosine of its complementary angle, and the cosine of an angle is equal to the sine of its complementary angle.

When looking at the unit circle What do you notice about the value of sin and the value of the Y-coordinate?

Defining Sine and Cosine Functions The sine function relates a real number t to the y-coordinate of the point where the corresponding angle intercepts the unit circle. More precisely, the sine of an angle t equals the y-value of the endpoint on the unit circle of an arc of length t. In Figure 2, the sine is equal to y.