One way to remember the trigonometric functions is through the acronym SOH CAH TOA. In the illustration above, we are shown what each respective side of the triangle is labeled, and now we can use this to apply to SOH CAH TOA.
SOH = sine, opposite, hypotenuse
CAH = cosine, adjacent, hypotenuse
TOA = tangent, opposite, adjacent
sinA = \frac{\text{y}}{\text{r}} = \frac{\text{opposite}}{\text{hypotenuse}}cscA = \frac{\text{r}}{\text{y}} = \frac{\text{hypotenuse}}{\text{opposite}}cosA = \frac{\text{x}}{\text{r}} = \frac{\text{adjacent}}{\text{hypotenuse}}secA = \frac{\text{r}}{\text{x}} = \frac{\text{hypotenuse}}{\text{adjacent}}tanA = \frac{\text{y}}{\text{x}} = \frac{\text{opposite}}{\text{adjacent}}cotA = \frac{\text{x}}{\text{y}} = \frac{\text{adjacent}}{\text{opposite}}Cofunction Identities
Cofunction identities are a set of trigonometric identities that relate the values of trigonometric functions of complementary angles (angles whose sum equals 90 degrees). In a right triangle, the two non-right angles are complementary.
sinA = cos(90\degree-A) \\ tanA = cot(90\degree - A) \\ secA = csc(90\degree - A)
For example:
sin30\degree = cos60\degree \\ tan45\degree = cot45\degree \\ sec60\degree = csc30\degree
As the angle theta increases, y increases, and x decreases.
This means that sin increases, cos decreases, and tan increases.
This isn’t too important to worry about though, just follow the math.
1.
sin25\degree > sin23\degree \\ \text{TRUE}2.
tan29\degree > cot36\degree \\ tan(90 \ - \ 36\degree) \\ tan29\degree > tan54\degree \\ \text{FALSE}