I learned trigonometric ratios this week. We have 3 trigonometric ratios and they are sine, cosine and tangent. Briefly sin, cos and tan. These are the ratios associated with the angles and sides of right triangles.

 

Here is a right triangle and the sides of this triangle have special names:

Yes, these names are hypotenuse, adjacent, opposite and we will use these names in trigonometric ratios.

 

These are expansions of trigonometric ratios:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent

 

And we have a reference angle. According to this reference angle, we determine the locations of hypotenuse, opposite and adjacent.

The reference angle for this triangle is t and accordingly the locations of the hypotenuse, opposite and adjacent are as follows.The names of these sides change places according to the reference angle.

For example, the names of the sides of this triangle according to the reference angle are as follows:

 

It’s time to use these trigonometric ratios. Here’s an example! Let’s find the trigonometric ratios of this right triangle.

 

First, we must name the sides of this right triangle. And according to what I explained above, this is how the sides are named.

 

Now we can write the ratios

This is the ratio table:

According to this:

sin = 33/65

cos = 56/65

tan = 33/56

 

 

Here is an another example. Let’s find the trigonometric ratios of this right triangle.

First, we name the sides.

 

Now we can write the ratios.

 

sin = 8/17

cos = 15/17

tan = 8/15