Trigonometric Functions Calculator
This trigonometric functions calculator can help in determining the values of six trig functions in no time. You'll find here not only the three basic functions  sine, cosine and tangent, but also their reciprocals: cosecant, secant and cotangent, respectively. Scroll down to read more about trigonometric ratios, to find sin cos tan charts and learn the mnemonic rule to remember functions definitions  sohcahtoa. Don't wait any longer, give this trigonometric functions calculator a try!
🔎 Trigonometric functions (sin, cos, tan) are all ratios. Therefore, you can find the missing terms using nothing else than our ratio calculator!
Sine, cosine, tangent...
Sine, cosine and tangent are the trigonometric function of an angle. If the angle is acute, you can define these trig functions in the context of a right triangle. Starting with the triangle sides nomenclature: we can name the sides of a right triangle as
 hypotenuse  probably you heard that term when learning about the Pythagorean theorem. So it's the longest side in the right triangle  the opposite one to the right angle (90°).
 adjacent side  the side forming the angle of interest (in our case, angle α), which is not a hypotenuse. This side is adjacent to both the angle of interest and the right angle.
 opposite side  the side opposite to the angle of interest (in this case, angle α).
Given the sides definitions, you can state that:
sin(α) = opposite / hypotenuse
sosin(α) = a / c
cos(α) = adjacent / hypotenuse
socos(α) = b / c
tan(α) = opposite / adjacent
sotan(α) = a / b
If you want to read more about those three famous functions, jump directly to our dedicated tools:
But if you don't care too much about the details, and just want to calculate all functions at once, use this tool as a complete sin cos tan calculator.
... And other trig functions: cosecant, secant and cotangent. Trigonometric ratios
In previous paragraph you learned about basic trigonometric ratios:
But what if we would like to invert the ratios? Like c / a
instead of a / c
? Apparently, these reciprocal trigonometric ratios have their own names, and are even used sometimes! So, for the right triangle:

Cosecant is the reciprocal of the sine
It's the ratio of the hypotenuse to the opposite. The abbreviation of cosecant is csc, e.g. csc(30°) and it's range is csc(α)≥ 1 and csc(α) ≤ 1:
csc(α) = 1 / sin(α) = c / a

Secant is the reciprocal of the cosine
It's the ratio of the hypotenuse to the adjacent. The abbreviation of secant is sec e.g. sec(30°) and it's range is sec(α)≥ 1 and sec(α) ≤ 1:
sec(α) = 1 / cos(α) = c / b

Cotangent is the reciprocal of the tangent
It's the ratio of the adjacent to the opposite side. The abbreviation of cotangent is cot, e.g. cot(30°) and it's range is ∞ < cot(α) < ∞:
cot(α) = 1 / tan(α) = b / a
If you think that's all trigonometric ratios, the six above  you're wrong. There are many other trig functions  like e.g. hacoversine, exsecant or versine  but, fortunately, they are archaic and obsolete, so not used nowadays. If you want to read more about those trigonometric functions used in dark precalculators ages, check out
by Evelyn Lamb from Scientific American Blog.Sohcahtoa (soh cah toa) mnemonics
Maybe you heard about that helpful sohcahtoa ("soakatoe", "sockatoa", "sokahtoa") mnemonic?

SOH stands for Sine equals Opposite over Hypotenuse.

CAH stands for Cosine equals Adjacent over Hypotenuse.

TOA stands for Tangent equals Opposite over Adjacent.
Trig function  Abbreviation  Definition 

Sine  SOH  sin(α) = opposite / hypotenuse 
Cosine  CAH  cos(α) = adjacent / hypotenuse 
Tangent  TOA  tan(α) = opposite / adjacent 
It's one of the methods to remember the definition of the basic trigonometric functions, but many other techniques exist. For example, you can simply pick one sentence which appeals to you the most:
 Sailors Often Have Curly Auburn Hair Till Old Age ⛵
 Some Old Horses Can Always Hear Their Owners Approach 🐎
 Some Old Hen Caught Another Hen Taking One Away 🐔
 Studying Our Homework Can Always Help To Obtain Achievement 📖
 Some Old Hippy Caught Another Hippy Tripping On Acid ☮️
Or invent your own, they are always the easiest to remember!
The trigonometric functions can also be defined in terms of the rise, run, and slope of a line segment relative to horizontal.
Charts of sin cos tan csc sec cot
Below you'll find the sin cos tan charts for <2π, 2π> range, as well as graphs for their reciprocal functions. And if you'd like to learn to play around with the shapes, make sure to check the phase shift calculator.
Sine  Cosecant 

Cosine  Secant 

Tangent  Cotangent 

How to use trigonometric functions calculator  an example
Are you still wondering how to use this trigonometric functions calculator? Don't worry; it's a piece of cake! 🍰
 Enter the angle. Choose between degrees and radians (in two versions rad or π rad). Let's take π/3 as an example, so choose π rad unit and type 1/3.
 Here it is! Six trig functions calculated by the trigonometric functions calculator in the blink of an eye! And also an explanatory image, if the angle is acute. What more can you ask, right?
What next?
Now that you have explored six trigonometric functions you might have fallen in love with trigonometry and want to dive deeper into the subject. For that we recommend checking out the
. A great collection of resources to help you improve your math knowledge and understanding.Or maybe you've had enough trigonometry for today and you're ready for more advanced topics, such as law of sines and law of cosines.
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