Trigonometry is one of the areas that students have the most difficult time. There is just so much to
know all the time and it isn't well incorporated in other units of mathematics in high school. So it's
easy to just "learn it for the moment". In advanced calculus, however, trigonometry tends to play a vital rule in topics such as integration, which is the second half of calculus.
Here I am going to review one of the two special triangles that should be in your mind for calculus and we
will practice with SOHCAHTOA, a rule which helps you in calculating the 3 primary trig ratios.
Right above I have drawn one of the two special triangles students taking calculus are expected to
memorize. Let's calculus the "sine" of the angle at "pi over 3". From SOHCAHTOA, we have S
involved for sine. S comes with OH so we will need to divide the opposite side of by the hypotenus.
To identify the opposite side, draw an arrow away from the angle and the side it points to is
your opposite, as shown below.
The hypotenuse side is always the side opposite to the 90 degree angle as shown here.
Now it's time to divide the two numbers involved to get our answer:
Let's do another calculation with this triangle: Compute
Here our reference angle has changed and, as a result, so will the labelling of some of the sides.
Remember, the opposite side is the side your arrow would point to when you start at your reference angle.
In the triangle above, two of the sides are labelled and are easy to identify with arrows, as shown.
The one side, with value , I didn't label will be our "adjacent side". Following sohcahtoa, to get
the "tan" of an angle, we divide the opposite side by the adjacent side.
For your reference, here is the other special triangle you are expected to know in calculus.
