The word trigonometry often strikes fear into a young students heart. Many students struggle with this area of math, but often times they are so terrified by the word trigonometry that they can’t even attempt the problems. Trigonometry doesn’t have to be that way. Once you memorize some key concepts and the special angle triangles, trigonometry won’t seem so scary.
SOHCAHTOA
Remembering SOHCAHTOA will give you a huge advantage when presented with trigonometric problems as it is a tool used to remember what sine, cosine, and tangent are equal to. In order to understand this you look at the letters in groups of three. The first letter let’s you know which operation to use (ie. S, C, and T are for sine, cosine, and tangent). The last two letters let you know what the operation means. The three letters are O. A, and H which mean opposite, adjacent, and hypotenuse, respectively. First we will look at the first three letters: SOH. The ‘S’ means sine, the O means opposite, and the H means hypotenuse. Remembering this is helpful because the sine of x is equal to the opposite side length divided by the hypotenuse side length:
sin(x) = O/H
We apply the same method to see that ‘CAH’ represents the cosine of x is equal to the adjacent side length divided by the hypotenuse side length and ‘TOA’ means that the tangent of x is equal to the opposite side length divided by the adjacent side length:
cos(x) = A/H
tan(x) = O/A
Special Angle Triangles
Special angle triangles refer to two triangles: one of which has inner angles 90º, 60º, and 30º and the other is an isosceles triangle with inner angles of 90º and 45º in the other two corners.
So, for example, if you wanted to find the sine of A, you would need to use the formula that SOHCAHTOA helps us remember. This means that sin(A) = a/c. This also means that cos(A) = b/c and tan(A) = a/b. Below is a chart of all the special angles and the operations on them. It’s good practice try and find them on your own in order to verify the chart.
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This article was written for you by Troy, one of the tutors with Test Prep Academy.