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Magazine Problem 8
Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. $$ y=-2 \cos \left(2 x-\frac{\pi}{2}\right) $$
Problem 8
Write down the exact value of each of the six trigonometric functions of \(30^{\circ}\) and of \(60^{\circ}\)
Problem 8
True or False The only trigonometric functions whose domain is all real numbers are the sine and cosine functions.
Problem 8
Which ratio is used to find \(\cot \theta ?\) (a) \(\frac{\text { opposite }}{\text { hypotenuse }}\) (b) \(\frac{\text { opposite }}{\text { adjacent }}\) (c) \(\frac{\text { adjacent }}{\text { opposite }}\) (d) \(\frac{\text { hypotenuse }}{\text { adjacent }}\)
Problem 8
True or False The graph of the sine function has infinitely many \(x\) -intercepts.
Problem 9
Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. $$ y=4 \sin (\pi x+2)-5 $$
Problem 9
Multiple Choice Which of the following is not in the range of the sine function? (a) \(\frac{\pi}{4}\) (b) \(\frac{3}{2}\) (c) \(-0.37\) (d) \(-1\)
Problem 9
True or False \(\tan \theta=\frac{\sin \theta}{\cos \theta}\)
Problem 9
True or False The angular speed \(\omega\) of an object traveling on a circle of radius \(r\) is the angle \(\theta\) (measured in radians) swept out, divided by the elapsed time \(t\).
Problem 9
In Problems \(9-18, f(\theta)=\sin \theta\) and \(g(\theta)=\cos \theta .\) Find the exact value of each expression if \(\theta=60^{\circ} .\) Do not use a calculator. $$ f(\theta) $$
