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Chapter 5: Problem 27
Write the expression as the sine, cosine, or tangent of an angle. $$\sin 3 \cos 1.2-\cos 3 \sin 1.2$$
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A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by $$y=\frac{1}{3} \sin 2 t+\frac{1}{4} \cos 2 t$$.where \(y\) is the distance from equilibrium (in feet) and \(t\) is the time (in seconds). (A). Use the identity \(a \sin B \theta+b \cos B \theta=\sqrt{a^{2}+b^{2}} \sin (B \theta+C)\) where \(C=\arctan (b / a), a>0,\) to write the model in the form \(y=\sqrt{a^{2}+b^{2}} \sin (B t+C)\). (B) Find the amplitude of the oscillations of the weight. (C) Find the frequency of the oscillations of the weight.
Prove the identity. $$\sin \left(\frac{\pi}{2}-x\right)=\cos x$$
Use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine. $$\sin ^{4} x \cos ^{2} x$$
Find all solutions of the equation in the interval \([0,2 \pi)\). $$\sin \left(x+\frac{\pi}{2}\right)-\cos ^{2} x=0$$
Write the expression as the sine, cosine, or tangent of an angle. $$\frac{\tan 45^{\circ}-\tan 30^{\circ}}{1+\tan 45^{\circ} \tan 30^{\circ}}$$
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