How to remember trigonometry ratios. Tip for remembering sin, cos and tan: Some Old Hags Can't Always Hide Their Old Age (sin = Opp/Hyp, cos = Adj/Hyp, tan = Opp/Adj) There were several replies which I thought you may enjoy (some are a bit racey and not very politically correct - you've been warned): From CardsChic: Oh Heck (sine) Another Hour 2.4K plays. 9th - 12th. explore. library. create. reports. classes. Tan, sin, and cos practice quiz for 9th grade students. Find other quizzes for Mathematics and more on Quizizz for free! In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calc Drag the point P around the curve into all 4 quadrants and observe the sin, cos and tan ratios that result. Notice in particular the ratios which are positive in each quadrant. Also, note that `sin theta` is defined as `y/r`, and `cos theta` is defined as `x/r` and `tan theta` is defined as `y/x`. Now we will divide sin x by cos x. (sin x) / (cos x) = [ (opposite) / (hypotenuse) ] / [ (adjacent) / (hypotenuse) ] = (opposite) / (adjacent) = tan x. Thus, the tangent formula in terms of sine and cosine is, tan x = (sin x) / (cos x) Tangent Formulas Using Pythagorean Identity. One of the Pythagorean identities talks about the relationship symmetry: since cos(-x) = cos (x) then cos (x) is an even function and its graph is symmetric with respect to the y axis. intervals of increase/decrease: over one period and from 0 to 2pi, cos (x) is decreasing on (0 , pi) increasing on (pi , 2pi). Tangent Function : f(x) = tan (x) Graph; Domain: all real numbers except pi/2 + k pi, k is an The graph of tangent is periodic, meaning that it repeats itself indefinitely. Unlike sine and cosine however, tangent has asymptotes separating each of its periods. The domain of the tangent function is all real numbers except whenever cos⁡(θ)=0, where the tangent function is undefined. This occurs whenever . This can be written as θ∈R Calculate Arcsine, Arccosine, Arctangent, Arccotangent, Arcsecant and Arccosecant for values of x and get answers in degrees, ratians and pi. Graphs for inverse trigonometric functions. Ucqhh6.