NSolve
(or Reduce
as pointed out by @ciao in the comments above) will find all solutions in a specified interval
$Version
"10.2.0 for Mac OS X x86 (64-bit) (July 7, 2015)"
NSolve[{5.20427*Sin[0.529699*t] == Sin[2*Pi*t], 0 <= t <= 100}, t]
{{t -> 0.}, {t -> 0.32491}, {t -> 5.97889}, {t -> 11.6173}, {t ->
12.1353}, {t -> 12.2205}, {t -> 17.9356}, {t -> 23.5697}, {t ->
29.8887}, {t -> 35.5261}, {t -> 41.1833}, {t -> 41.4872}, {t ->
41.8327}, {t -> 47.4839}, {t -> 53.1234}, {t -> 53.6101}, {t ->
53.7428}, {t -> 59.4409}, {t -> 65.075}, {t -> 71.3945}, {t ->
77.0312}, {t -> 82.6919}, {t -> 82.9743}, {t -> 83.3401}, {t ->
88.9889}, {t -> 94.6297}, {t -> 95.0909}, {t -> 95.2589}}
In some Mathematica versions there will be a warning message, e.g.,
$Version
"10.0 for Mac OS X x86 (64-bit) (June 29, 2014)"
NSolve[{5.20427*Sin[0.529699*t] == Sin[2*Pi*t], 0 <= t <= 100}, t]
Solve::ratnz: Solve was unable to solve the system with inexact
coefficients. The answer was obtained by solving a corresponding exact
system and numericizing the result. >>
{{t -> 0.}, {t -> 0.32491}, {t -> 5.97889}, {t -> 11.6173}, {t ->
12.1353}, {t -> 12.2205}, {t -> 17.9356}, {t -> 23.5697}, {t ->
29.8887}, {t -> 35.5261}, {t -> 41.1833}, {t -> 41.4872}, {t ->
41.8327}, {t -> 47.4839}, {t -> 53.1234}, {t -> 53.6101}, {t ->
53.7428}, {t -> 59.4409}, {t -> 65.075}, {t -> 71.3945}, {t ->
77.0312}, {t -> 82.6919}, {t -> 82.9743}, {t -> 83.3401}, {t ->
88.9889}, {t -> 94.6297}, {t -> 95.0909}, {t -> 95.2589}}
This warning can be avoided by using Rationalize
NSolve[{5.20427*Sin[0.529699*t] == Sin[2*Pi*t] // Rationalize[#, 0] &,
0 <= t <= 100}, t]
Reduce[520427/100000*Sin[529699/1000000*t] - Sin[2*Pi*t] == 0 && 0 <= t <= 100, t, Reals] // N
with some reasonable bound on t might get you what you're after... $\endgroup$NSolve[{5.20427*Sin[0.529699*t] == Sin[2*Pi*t] // Rationalize[#, 0] &, 0 <= t <= 100}, t]
$\endgroup$