Additional Math – Trigonometry – Using the R-Formula to Change a Trigonometric Expression

Additional Math - Trigonometry - Using the R-Formula to Change a Trigonometric Expression

$latex \displaystyle 10{{\cos }^{2}}x+4{{\sin }^{2}}x+8\sin x\cos x$
Split 10 cos2x and factorize 8sinxcosx.
$latex \displaystyle 6{{\cos }^{2}}x+4{{\cos }^{2}}x+4{{\sin }^{2}}x+4\left( {2\sin x\cos x} \right)$

Change 2sinxcosx to sin2x (Sine Double Angle Formula)

 

$latex \displaystyle 3(2{{\cos }^{2}}x)+4({{\cos }^{2}}x+{{\sin }^{2}}x)+4\sin 2x$

Change 2cos2x to cos2x+1 (Cosine Double Angle Formula)

 

$latex \displaystyle 3(\cos 2x+1)+4+4\sin 2x$

 

$latex \displaystyle 7+4\sin 2x+3\cos 2x$

 

$latex \displaystyle R=\sqrt{{{{4}^{2}}+{{3}^{2}}}}=5$

 

$latex \displaystyle \tan \alpha =\frac{3}{4},\ \alpha ={{\tan }^{{-1}}}\frac{3}{4}={{36.9}^{o}}$

 

$latex \displaystyle y=7+5\left[ {\sin (2x+{{{36.9}}^{o}}} \right]$

Additional Math (A Math) (a Math) Tuition in Woodlands and Johor Bahru. 

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