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Magazine Problem 82
In Exercises \(67-94,\) add the ordinates of the individual functions to graph each summed function on the indicated interval. $$y=\sin \left[\frac{\pi}{4}(x+2)\right]+3 \cos \left[\frac{3 \pi}{3}(x-1)\right], 1 \leq x \leq 5$$
Problem 83
What is the amplitude of the function \(y=\cos x+\sin x ?\) Use a graphing calculator to graph \(Y_{1}=\cos x, Y_{2}=\sin x\) and \(Y_{3}=\cos x+\sin x\) in the same viewing window.
Problem 83
Use a calculator to approximate \(\sin 423^{\circ} .\) What do you expect \(\sin \left(-423^{\circ}\right)\) to be? Verify your answer with a calculator.
Problem 83
In Exercises \(67-94,\) add the ordinates of the individual functions to graph each summed function on the indicated interval. $$y=\cos \left(\frac{x}{2}\right)+\cos (2 x), 0 \leq x \leq 4 \pi$$
Problem 84
In Exercises \(67-94,\) add the ordinates of the individual functions to graph each summed function on the indicated interval. $$y=\sin (2 x)+\sin (3 x),-\pi \leq x \leq \pi$$
Problem 84
Use a calculator to approximate \(\cos 227^{\circ} .\) What do you expect \(\cos \left(-227^{\circ}\right)\) to be? Verify your answer with a calculator.
Problem 85
What is the period of the function \(y=\tan x+\cot x ?\) Use a graphing calculator to graph \(Y_{1}=\tan x+\cot x\) and \(Y_{3}=2 \csc (2 x)\) in the same viewing window.
Problem 85
Use a calculator to approximate \(\tan 81^{\circ} .\) What do you expect \(\tan \left(-81^{\circ}\right)\) to be? Verify your answer with a calculator.
Problem 85
In Exercises \(67-94,\) add the ordinates of the individual functions to graph each summed function on the indicated interval. $$y=\sin \left(\frac{x}{2}\right)+\sin (2 x), 0 \leq x \leq 4 \pi$$
Problem 86
Use a calculator to approximate cse \(211^{\circ} .\) What do you expect \(\csc \left(-211^{\circ}\right)\) to be? Verify your answer with a calculator.
