Sin Cos Tan Csc Sec Cot Chart
Camila Farah
For an angle in standard position we define the trigonometric ratios in terms of x y and r.
Sin θ as opp hyp. Here is the table with the values of trigonometric ratios for standard angles. Note sec x is not the same as cos 1 x sometimes written as arccos x. Trigonometric ratios sin cos tan cot sec and cosec these six trigonometric ratios form the base of trigonometry.
So learn them carefully. Tan 300 my teacher gave us the unit circle chart and a chart of the basic values for sin cos tan csc sec cot for 0 30 45 60 and 90 degrees for example cos of 30 degrees sq rt 3 2. But we are using the specific x y and r values defined by the point x y that the terminal side passes through. Sin 1 y q y 1 csc y q cos 1 x q x 1 sec x q tan y x q cot x y q facts and properties domain the domain is all the values of q that can be plugged into the function.
As we saw above tan x sin x cos x this means the function will have a discontinuity where cos x 0. The reason tan and cot repeat after only pi radians is because when dividing sin and cos to get tan we get the same values in quadrants iii as iv as we do for quadrants i and ii. We have angle and in. Sin theta y r cos theta x r tan theta y x notice that we are still defining.
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Sketch y tan x. Remember you cannot divide by zero and so these definitions are only valid when the denominators are not zero. Adjacent side to angle is bc and adjacent side to. Graphs of sec x and cosec x.
Tan sin cos cosec 1 sin 1 sec 1 cos 1 cot 1 tan 1. Lets suppose we have triangle abc right angled at b. That is when x takes any. Don t forget to try our free app agile log which helps you track your time spent on various projects and tasks try it now.
Cot x 1 cos x tan x sin x. The sin and cos and csc and sec functions start repeating after 2 pi radians and it turns out that the tan and cot functions start repeating again after only pi radians. If sec x 2 cos x x 60º. Cos θ as adj hyp and.
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The same thing happens with cot x sec x and csc x for different values of x. Cos hypotenuse q hypotenuse sec adjacent q opposite tan adjacent q adjacent cot opposite q unit circle definition for this definition q is any angle. Tan θ as opp adj. Trignometry table of sin cos tan cosec sec cot is useful to learn the common angles of trigonometrical ratios are 0 30 45 60 90 180 270 and 360.
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