91Ó°ÊÓ

Simplify the given expressions. The result will be one of \(\sin x, \cos x, \tan x, \cot x, \sec x,\) or \(\csc x\). $$\cot x(\sec x-\cos x)$$

Solve the indicated equations analytically. Find the angles of a triangle if one side is twice another side and the angles opposite these sides differ by \(60^{\circ}\)

Solve the given problems. Express \(\sin 3 x\) in terms of \(\sin x\) only.

Use the half-angle formulas to solve the given problems. In electronics, in order to find the root-mean-square current in a circuit, it is necessary to express \(\sin ^{2} \omega t\) in terms of \(\cos 2 \omega t .\) Show how this is done.

Simplify the given expressions. The result will be one of \(\sin x, \cos x, \tan x, \cot x, \sec x,\) or \(\csc x\). $$\sin x(\tan x+\cot x)$$

Solve the indicated equations analytically. If two musical tones of frequencies \(220 \mathrm{Hz}\) and \(223 \mathrm{Hz}\) are played together, beats will be heard. This can be represented by \(y=\sin 440 \pi t+\sin 446 \pi t .\) Graph this function and estimate \(t\) (in s) when \(y=0\) between beats for \(0.15

Use the half-angle formulas to solve the given problems. In studying interference patterns of radio signals, the expression \(2 E^{2}-2 E^{2} \cos (\pi-\theta)\) arises. Show that this can be written as \(4 E^{2} \cos ^{2}(\theta / 2)\)

Express \(\cos 3 x\) in terms of \(\cos x\) only.

Solve the given problems. Express \(\cos 3 x\) in terms of \(\cos x\) only.

Solve the given problems. The design of a certain three-phase alternating-current generator uses the fact that the sum of the currents \(I \cos \left(\theta+30^{\circ}\right)\) \(I \cos \left(\theta+150^{\circ}\right),\) and \(I \cos \left(\theta+270^{\circ}\right)\) is zero. Verify this.