You can see by the listing that cotangent (abbreviated cot, or sometimes ctn) is the reciprocal of tangent, secant (abbreviated sec) is the reciprocal of cosine, and cosecant (abbreviated csc, or sometimes cosec) is the reciprocal of sine. There are six ways of making ratios of two sides of a right triangle, and that gives the six functions: You might ask, “why six trig functions?” It’s a kind of symmetry.
There are, however, cases when some others are needed. The other three trigonometric functions: cotangent, secant, and cosecantįor most purposes the three trig functions sine, cosine, and tangent are enough. (If you like, you can convert the 0.79 degrees to minutes and seconds.) The arctangent of 0.2455 is 13.79, so the angle A is 13.79°.
Usually there’s a button on the calculator labelled “inv” or “arc” that you press before pressing the appropriate trig button. On a calculator, we use the inverse trig functions named arctangent, arcsine, and arccosine. Back when people used tables of trig functions, they would just look up in the tangent table to see what angle had a tangent of 0.2455. Again, you use the trig functions, but in reverse. Now let’s look at the problem of finding angles if you know the sides. Inverse trig functions: arcsine, arccosine, and arctangent Whether you use a sine, cosine, or tangent depends on which side and angle you know. For example, if the side a = 15 and the angle A = 41°, we can use a sine and a tangent to find the hypotenuse and the other side. We might only know one side but we also know an angle. Now suppose we know the hypotenuse and one side, but have to find the other.
(It’s nice to give examples where the square roots come out whole numbers in life they usually don’t.) The Pythagorean theorem will give us the hypotenuse. Suppose we don’t know the hypotenuse but we do know the other two sides. Let’s first look at some cases where we don’t know all the sides. We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts.
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