So sine and cosine calculations are only calculate on the acute non-right angles of triangles. Is that correct?
This from math2.org:
Definition 1 Given any angle q (0 £ q £ 90°), we can find the sine or cosine of that angle by constructing a right triangle with one vertex of angle q. The sine is equal to the length of the side opposite to q, divided by the length of the triangle's hypotenuse. The cosine is equal to the length of the side adjacent to q, divided by the length of the triangle's hypotenuse. In this way, we can find the sine or cosine of any q in the range 0 £ q £ 90°.
Definition 2 Draw a unit circle, in that a circle of radius 1, centered at the origin of a 2-dimensional coordinate system. Given an angle q, locate the point on the circle that is located at an angle q from the origin. (According to standard convention, angles are measured counter-clockwise from the positive horizontal axis.) The sin(q) can be defined as the y-coordinate of this point. The cos(q) can be defined as the x-coordinate of this point. In this way, we can find the sine or cosine of any real value of q (q Î Â).
So my questions:
- What are the sin and cosine exactly? Do you only calculate the sine and cosine of right triangles? What do you if the triangle is not right? Are there still relationships between the sides given an angle?
- When you calculate sin(85 degrees), what exactly are we calculating? Are we calculating the opposite side/hypotenuse of a right triangle?