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Magazine Problem 85
For the following expressions, find the value of \(y\) that corresponds to each value of \(x\), then write your results as ordered pairs \((x, y)\). \(y=\sin 2 x \quad\) for \(x=0, \frac{\pi}{4}, \frac{\pi}{2}, \frac{3 \pi}{4}, \pi\)
Problem 86
For the following expressions, find the value of \(y\) that corresponds to each value of \(x\), then write your results as ordered pairs \((x, y)\). \(y=\cos 3 x \quad\) for \(x=0, \frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{2}, \frac{2 \pi}{3}\)
Problem 86
If the two shorter sides of a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle are both \(\frac{3}{4}\), find the length of the hypotenuse.
Problem 86
Describe how cot \(t\) varies as \(t\) increases from 0 to \(\pi / 2\).
Problem 87
For the following expressions, find the value of \(y\) that corresponds to each value of \(x\), then write your results as ordered pairs \((x, y)\). \(y=\sin \left(x-\frac{\pi}{2}\right) \quad\) for \(x=\frac{\pi}{2}, \pi, \frac{3 \pi}{2}, 2 \pi, \frac{5 \pi}{2}\)
Problem 87
Describe how \(\sin t\) varies as \(t\) increases from \(\pi / 2\) to \(\pi\).
Problem 88
For the following expressions, find the value of \(y\) that corresponds to each value of \(x\), then write your results as ordered pairs \((x, y)\). \(y=\cos \left(x-\frac{\pi}{6}\right) \quad\) for \(x=\frac{\pi}{6}, \frac{\pi}{3}, \frac{2 \pi}{3}, \pi, \frac{7 \pi}{6}\)
Problem 88
Describe how \(\cos t\) varies as \(t\) increases from \(\pi / 2\) to \(\pi\).
Problem 88
Simplify each expression by substituting values from the table of exact values and then simplifying the resulting expression. $$ 4 \sin 60^{\circ}-2 \cos 30^{\circ} $$
Problem 89
For the following expressions, find the value of \(y\) that corresponds to each value of \(x\), then write your results as ordered pairs \((x, y)\). \(y=2+\cos x \quad\) for \(x=0, \frac{\pi}{2}, \pi, \frac{3 \pi}{2}, 2 \pi\)
