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-------------------------xxxxx---------------------- Trigonometric Equations Here's a very quick outline of what's been introduced in this tutorial :
Example: Consider the equation : 2sinx=3^{0.5} We solve it to get: sin x=3^{0.5}/2 Or, x=π/3,2π/3,4π/3,…
sin x = sin y cos x =cos y tan x = tan y For solving these equations, we need to be familiar with the solutions of equations: sin x=0, cos x=0, cot x=0.
sin x=sin y
=>sin x-sin y=0 =>2sin(x-y)/2 cos(x+y)/2=0 =>sin (x-y)/2=0 or cos(x+y)/2=0 =>x-y=2nπ or x+y=(2m+1)π, m, nεZ =>x=2nπ+y or x=(2m+1)π =>x=(even multiple of π)+y or (odd multiple of π)-y =>x=nπ+(-1)ny, nεZ The solutions of cosec x= cosec y are also the same.
cos x= cos y Following the similar procedure, we get
-2sin(x+y)/2 sin (x-y)/2=0. =>x+y=2nπ or x-y=2mπ =>x=2nπ±y, nεZ sec x=sec y has the same solution.
tan x=tan y =>sin x cos y=sinycosx =>sin(x-y)=0 =>x-y=nπ =>x=nπ+y , nεZ cot x=cot y has the same solution
Here are the kind of questions which have been solved in this tutorial : Solve sin5x=0; x is in the range of 0 to π Solve sin x+ sin 3x+sin 5x=0 Solve sin nx +cos mx=0. Solve sin3x+cos2x=0Solve cot2x+3/sinx+3=0 Solve sin2x=sin2y, and tan2x=tan2y Solve √3cosx+sinx=√2 Solve for general x, y sin (x – y) = 2 sin x sin y, where x and y are two acute angles of right angle triangle. Solve the equation sin4 x + cos4 x = 7/2 sinx cosx Complete Tutorial (To test how much you know, try out our Quiz at the end):MCQ Quiz #1Companion MCQ Quiz for Trigonometric Equations (Basic Problems) - test how much you know about the topic ! Your score will be e-mailed to you at the address you provide. MCQ Quiz #2Companion MCQ Quiz for Trigonometric Equations (More Challenging Problems) - test how much you know about the topic ! Your score will be e-mailed to you at the address you provide. |
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