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Item 1. Formula Sheet-PC Math 12. Below is the formula sheet for this course, as found in the course intro. You will be provided this within all quizzes and tests for your use. You can click back to this location to make use of the information as needed throughout the test.
This item is a formula sheet download/reference item. No calculation is required for this item. Use the formula sheet as needed throughout the quiz. Answer: N/N
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Item 2. A right angle triangle has a hypotenuse of \(25\) inches. If one angle has a measure of \(49^\circ\), what is the measure of the side opposite that angle? Give your answer to one decimal place.
Use the sine ratio because the opposite side and hypotenuse are involved. \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\) \(\sin 49^\circ=\frac{\text{opposite}}{25}\) \(\text{opposite}=25\sin 49^\circ\) \(\text{opposite}\approx 18.9\text{ in}\) Therefore the side opposite the angle is \(18.9\text{ in}\). Answer: D
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Item 4. Which of the following shows an angle of \(315^\circ\) in standard position? [Graphs will be inserted later.]
An angle in standard position starts on the positive \(x\)-axis. A positive angle rotates counterclockwise. \(315^\circ\) is greater than \(270^\circ\) and less than \(360^\circ\). Therefore the terminal arm lies in Quadrant IV. The graph that shows a \(315^\circ\) angle in standard position is Graph B. Answer: B
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Item 3. Determine the reference angle for \(215^\circ\) in standard position.
The angle \(215^\circ\) is in Quadrant III. The reference angle is the positive acute angle between the terminal arm and the \(x\)-axis. In Quadrant III, subtract \(180^\circ\) from the given angle. \(\text{Reference Angle}=215^\circ-180^\circ=35^\circ\) Therefore the reference angle is \(35^\circ\). Answer: A
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Item 5. Which pair of angles are coterminal with \(\frac{5\pi}{3}\) radians?
Coterminal angles differ by integer multiples of \(2\pi\). Start with \(\frac{5\pi}{3}\). Add \(2\pi=\frac{6\pi}{3}\): \(\frac{5\pi}{3}+\frac{6\pi}{3}=\frac{11\pi}{3}\). Subtract \(2\pi=\frac{6\pi}{3}\): \(\frac{5\pi}{3}-\frac{6\pi}{3}=-\frac{\pi}{3}\). Therefore the coterminal pair is \(-\frac{\pi}{3}\) and \(\frac{11\pi}{3}\). Answer: D
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Item 6. Consider the graph: \(y=\sin\theta\) where \(-2\pi\leq\theta\leq2\pi\). For what value(s) of \(\theta\) does \(\sin\theta=0\)?
The zeros of \(y=\sin\theta\) occur where the graph crosses the \(\theta\)-axis. \(\sin\theta=0\) at integer multiples of \(\pi\). Within \(-2\pi\leq\theta\leq2\pi\), these values are: \(\theta=-2\pi,-\pi,0,\pi,2\pi\). Therefore the correct set of values is \(-2\pi,-\pi,0,\pi,2\pi\). Answer: D
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Item 7. Consider the graph: \(y=\cos\theta\) where \(-2\pi\leq\theta\leq2\pi\). For what value(s) of \(\theta\) does \(\cos\theta=0\)?
The zeros of \(y=\cos\theta\) occur where the graph crosses the \(\theta\)-axis. \(\cos\theta=0\) at odd multiples of \(\frac{\pi}{2}\). Within \(-2\pi\leq\theta\leq2\pi\), these values are: \(\theta=-\frac{3\pi}{2},-\frac{\pi}{2},\frac{\pi}{2},\frac{3\pi}{2}\). Therefore the correct set of values is \(-\frac{3\pi}{2},-\frac{\pi}{2},\frac{\pi}{2},\frac{3\pi}{2}\). Answer: B
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