SOHCAHTOA (pronounced: so-cah-tow-ah) is a very useful mnemonic that can help students remember the sine ratio, cosine ratio, and the tangent ratio of the three basic trigonometric functions sine, cosine, and tangent.
SOH : Sine = Opposite / Hypotenuse
CAH : Cosine = Adjacent / Hypotenuse
TOA : Tangent = Opposite / Adjacent
As you can see in the image below, the sides of a right triangle are the opposite side, the adjacent side, and the hypotenuse.
Study the nice figure shown above carefully! It will help you greatly to remember the acronym sohcahtoa, which is a memory aid that can help you the following important ratios
sin θ = opposite side / hypotenuse
cos θ = adjacent side / hypotenuse
tan θ = opposite / adjacent
You could also use the following mnemonic to remember the trigonometric ratios.
" Some Old Hog Came Around Here and Took Our Apples."
Example #1
Use the triangle below to find the values of sin θ, cos θ, and tan θ
sin(θ) = opposite side / hypotenuse = 6/10 = 0.6
cos(θ) = adjacent side / hypotenuse= 8/10 = 0.8
tan(θ) = opposite / adjacent = 6/8 = 0.75
Example #2
Use the triangle below to find the values of sin θ, cos θ, tan θ, csc θ, sec θ, and cot θ
First, we need to find the length of the hypotenuse using the Pythagorean theorem.
c^{2} = 152 + 82
c^{2} = 225 + 64
c^{2} = 289
c = √289
c = 17
sin(θ) = opposite side / hypotenuse = 8/17
cos(θ) = adjacent side / hypotenuse = 15/17
tan(θ) = opposite / adjacent = 8/15
csc(θ) = hypotenuse / opposite side = 17/8
sec(θ) = hypotenuse / adjacent side = 17/15
cot(θ) = adjacent / opposite = 15/8