Math  /  Trigonometry

QuestionIf sinu=x6\sin u=\frac{x}{6}, express 4sinu+cosu4 \sin u+\cos \boldsymbol{u} in terms of x\boldsymbol{x}. Assume 0<u<π20<\boldsymbol{u}<\frac{\pi}{2}.

Studdy Solution
Sustituir sinu \sin u y cosu \cos u en la expresión 4sinu+cosu 4 \sin u + \cos u .
4sinu+cosu=4(x6)+1x236 4 \sin u + \cos u = 4 \left(\frac{x}{6}\right) + \sqrt{1 - \frac{x^2}{36}}
=4x6+1x236 = \frac{4x}{6} + \sqrt{1 - \frac{x^2}{36}}
=2x3+1x236 = \frac{2x}{3} + \sqrt{1 - \frac{x^2}{36}}
La expresión 4sinu+cosu 4 \sin u + \cos u en términos de x x es:
2x3+1x236 \boxed{\frac{2x}{3} + \sqrt{1 - \frac{x^2}{36}}}

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