How to solve this trigonometric equation?

Question

I am a new user of Mathematica. I want to solve the following equation

a*Tan[a] = Sqrt[(52.7531 - a^2)]

for a, where a is a real value. I used the Solve function, but I am not getting the right answer.

I tried,

Solve[a*Tan[a] == Sqrt[(52.7531 - a^2)], a, Reals]

I am doing something wrong. Could anyone tell me what it is? Thanks in advance.

1. Reformulate your equation to be singularity-free. 2. Provide bounds, since you don't actually want infinitely many roots. Thus: Solve[a Sin[a] == Sqrt[(52.7531 - a^2)] Cos[a] && -7 < a < 7, a, Reals] — J. M.'s missing motivation, Commented Oct 1, 2017 at 7:40
J.M., thanks a lot for pointing out the things I had missed. Got it now! :) — Aashiek Hariharan, Commented Oct 1, 2017 at 7:52
Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! — Michael E2, Commented Oct 1, 2017 at 12:00

user64494 · Accepted Answer · 2017-10-01 07:43:18Z

3

The result of

Plot[a*Tan[a] - Sqrt[(52.7531 - a^2)], {a, -7, 7}]

suggests

NSolve[a*Tan[a] == Sqrt[(52.7531 - a^2)] && a > -7 && a < 7, a]

{{a->-6.68491},{a->-4.11077},{a->-1.37968},{a->1.37968},{a->4.11077},{a->6.68491}}

answered Oct 1, 2017 at 7:34

user64494

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$\begingroup$ user6444, thanks a lot, mate! That solved the issue! :) $\endgroup$
– Aashiek Hariharan
Commented Oct 1, 2017 at 7:54

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