Sin, cos, and tan are trigonometric ratios that relate the angles and sides of right triangles. Sin is the ratio of the opposite side to the hypotenuse, cos is the ratio of the adjacent side to the hypotenuse, …

Sine, cosine, and tangent represent ratios of right triangle side lengths. This means if we have the value of the sine, cosine, or tangent of an angle and one side length, we can find the other side lengths.

As you see above, by definition, the hypotenuse is always the longest side in a right triangle and is always opposite the right angle. An adjacent side is any side that is, well, adjacent to a given angle, …

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In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.

For example, a right angled triangle with one of the angles measuring 51º will always have the same ratio for that angle's opposite and adjacent edges, no matter how large or small the triangle is.

The adjacent side in a right triangle is the side that is touching the reference angle that isn't the hypotenuse. The opposite side is the side that is, well, the side the angle is opening up to.

If they happen to be adjacent, then the two outside sides will form a right angle. When you have a right angle, the two sides of a right angle are considered to be perpendicular.

Since we know all of our side lengths now, we just need to use the inverse functions to calculate our angles. Let's find out angle O: angle O is adjacent to line OE, opposite of line ZE, and our …

And let's just say that the cosine of our angle is equal to the x-coordinate where we intersect, where the terminal side of our angle intersects the unit circle. And why don't we define sine of theta to be equal …