= tan ^ -1 (0.55431) = approximately 29 degrees
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ArcTan is another name for ;Inverse Tan' or 'Tan^*-1) Hence ArcTan(0.55431) = 29.00004157 degrees. Effectively 29 degrees.
Assuming that neither of the given sides is the hypotenuse, then if A is one of the acute angles, tan(A) = 19/63 So A = arctan(19/63) = 16.8 degrees. The other acute angle is 73.2 deg.
Trigonometric functions are periodic so they are many-to-one. It is therefore important to define the domains and ranges of their inverses in such a way the the inverse function is not one-to-many. Thus the range for arcsin is [-pi/2, pi/2], arccos is [0, pi] and arctan is (-pi/2, pi/2). However, these functions can be used, along with the periodicities to establish relations which extend solutions beyond the above ranges.
Assume the angle u takes place in Quadrant IV. Let u = arctan(-12). Then, tan(u) = -12. By the Pythagorean identity, we obtain: sec(u) = √(1 + tan²(u)) = √(1 + (-12)²) = √145 Since secant is the inverse of cosine, we have: cos(u) = 1/√145 Therefore: sin(u) = -√(1 - cos²(u)) = -√(1 - 1/145) = -12/√145 Otherwise, if the angle takes place in Quadrant II, then sin(u) = 12/√145
Well, darling, if tangent k equals 0.575, then angle k is approximately 29.74 degrees. Just remember to use your trusty calculator and make sure it's in the correct mode before you go crunching those numbers. Happy calculating, honey!