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Magazine Problem 84
In Exercises 81-84, determine whether each statement is true or false. $$ \cos \theta=1 \text { when } \theta=n \pi \text {, for } n \text { an integer. } $$
Problem 84
$$ \text { In Exercises 59-84, find the exact value of the following expressions. Do not use a calculator. } $$ $$ \sin \left(-\frac{8 \pi}{3}\right) $$
Problem 85
$$ \text { For Exercises } 85 \text { and 86, refer to the following: } $$ Two electronic signals that are not co-phased are called out of phase. Two signals that cancel each other out are said to be \(180^{\circ}\) out of phase, or the difference in their phases is \(180^{\circ}\). Electronic Signals. How many radians out of phase are two signals whose phase difference is \(270^{\circ}\) ?
Problem 85
$$ \text { Is } y=\csc x \text { an even or an odd function? Justify your answer. } $$
Problem 86
$$ \text { Is } y=\tan x \text { an even or an odd function? Justify your answer. } $$
Problem 86
$$ \text { For Exercises } 85 \text { and 86, refer to the following: } $$ Two electronic signals that are not co-phased are called out of phase. Two signals that cancel each other out are said to be \(180^{\circ}\) out of phase, or the difference in their phases is \(180^{\circ}\). Electronic Signals. How many radians out of phase are two signals whose phase difference is \(110^{\circ}\) ?
Problem 87
Find all the values of \(\theta, 0 \leq \theta \leq 2 \pi\), for which the equation is true: \(\sin \theta=\cos \theta\).
Problem 87
$$ \text { For Exercises } 85 \text { and 86, refer to the following: } $$ Two electronic signals that are not co-phased are called out of phase. Two signals that cancel each other out are said to be \(180^{\circ}\) out of phase, or the difference in their phases is \(180^{\circ}\). Construction. In China, you find circular clan homes called tulou. Some tulou are three or four stories high and exceed 70 meters in diameter. If a wedge or section on the third floor of such a building has a central angle measuring \(36^{\circ}\), how many radians is this?
Problem 88
Find all the values of \(\theta\) ( \(\theta\) is any real number) for which the equation is true: \(\sin \theta=\cos \theta\).
Problem 88
$$ \text { For Exercises } 85 \text { and 86, refer to the following: } $$ Two electronic signals that are not co-phased are called out of phase. Two signals that cancel each other out are said to be \(180^{\circ}\) out of phase, or the difference in their phases is \(180^{\circ}\). Construction. In China, you find circular clan homes called tulou. Some tulou are three or four stories high and exceed 70 meters in diameter. If a wedge or section on the third floor of such a building has a central angle measuring \(72^{\circ}\), how many radians is this?
