5.1 Phy1020: brief trigonometry tutorial  (Page 8/20)

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The value for the sine of the angle is then used in an algebraic equation to compute the length of the opposite side, which is displayed in Figure 6 . (This equation is one of the equations shown in Figure 7 .)

Looks very close to me

As you can see, the computed value for the opposite side shown in Figure 6 is extremely close to the known value of 4 units.

Re-compute the length of the hypotenuse

After that, the value of the hypotenuse is re-computed (as though it were the unknown in the problem) using the value of the sine and the recently computedvalue of the opposite side. (Once again, one of the equations from Figure 7 is used to perform the computation.) The output length for the hypotenuse is shown in Figure 6 , and it matches the known value.

Example usage of Math.asin and Math.sin methods

Listing 2 and Listing 3 provide examples of how to use the JavaScript Math.asin and Math.sin methods to find the angle, the opposite side, or the hypotenuse of a right triangle when the other two areknown as shown by the equations in Figure 7 .

The cosine and arccosine of an angle

You are going to find the discussion in this section to be very similar to the discussion in the previous section on the sine and the arcsine of an angle.

Once again, although the cosine of an angle is based on very specific geometric considerations involving circles (see (External Link) ), for our purposes, the cosine of an angle is simply a ratio between the lengths of two different sides of a righttriangle.

A ratio of two sides

For our purposes, we will say that the cosine of an angle is equal to the ratio of the adjacent side and the hypotenuse. Therefore, in the case of the3-4-5 triangle that you have on your graph board, the cosine of the angle at the origin is equal to 3/5 or 0.6.

As before, if we know the lengths of the hypotenuse and the adjacent side, we can compute the cosine and use it to determine the value of the angle. (We willdo this later.)

Conversely, if we know the value of the angle but don't know the lengths of the hypotenuse and/or the adjacent side, we can obtain the cosine value (theratio of the adjacent side and the hypotenuse) using a scientific calculator or lookup table and use it for other purposes later.

The cosine of an angle -- sample computation

Enter the following into the Google search box:

cos(53.13010235415598 degrees)

The following will appear immediately below the search box:

cos(53.13010235415598 degrees) = 0.6

This matches the ratio of the adjacent side to the hypotenuse for a 3-4-5 triangle.

The arccosine (inverse cosine) of an angle

The arccosine of an angle is the value of the angle having a given cosine value. In other words, if you know the value of the cosine of an unknown angle,you can use a scientific calculator or lookup table to find the value of the angle.

Getting the angle for a known cosine value

For example, we know that the cosine of the angle at the origin on your graph board is 0.6. From that, we can determine the value of the angle using eitherthe Google calculator or JavaScript.

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