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Solving trigonometric equations

  • Thread starter teng125
  • Start date
416
0
as we know that (sin(x))^2 + (cos(x))^2=1
how about (sin(3x))^2 + (cos(3x))^2 and 5sin(3x)^2 + 6cos(3x)^2??

how can we solve these problems??
thanx
 
86
0
What are you trying to solve? You could substitute numbers for the x's and compute the value.

I don't believe there's a nifty identity for (sin(3x))^2 + (cos(3x))^2 even though it does look somewhat similar to (sin(x))^2 + (cos(x))^2.
 
86
0
Actually, aslong as the arguments match it equals one. So (sin(3x))^2 + (cos(3x))^2 does equal one.
 

Hootenanny

Staff Emeritus
Science Advisor
Gold Member
9,598
6
Indeed, if we apply the identity [itex]\sin^{2}\theta +\cos^{2}\theta = 1[/itex],to the above expression and simply use the substitution [itex]3x = \theta[/itex].... :wink:
 

HallsofIvy

Science Advisor
Homework Helper
41,713
876
For 5sin(3x)^2 + 6cos(3x)^2, write it as 5sin^3(3x)+ 5cos^2(3x)+ cos^2(3x)= 5(sin^3(3x)+ cos^2(3x))+ cos^2(3x)= 5+ cos^2(3x).
 

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