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Chapter 4: Problem 63
What does it mean to solve a right triangle?
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although I can use an isosceles right triangle to determine the exact value of \(\sin \frac{\pi}{4},\) I can also use my calculator to obtain this value.
The number of hours of daylight, \(H,\) on day \(t\) of any given year (on January \(1, t=1\) ) in Fairbanks, Alaska, can be modeled by the function $$H(t)=12+8.3 \sin \left[\frac{2 \pi}{365}(t-80)\right]$$ a. March \(21,\) the 80 th day of the year, is the spring equinox. Find the number of hours of daylight in Fairbanks on this day. b. June \(21,\) the 172 nd day of the year, is the summer solstice, the day with the maximum number of hours of daylight. To the nearest tenth of an hour, find the number of hours of daylight in Fairbanks on this day. c. December \(21,\) the 355 th day of the year, is the winter solstice, the day with the minimum number of hours of daylight. Find, to the nearest tenth of an hour, the number of hours of daylight in Fairbanks on this day.
Write the point-slope form and the slope-intercept form of the line passing through \((-1,-2)\) and \((-3,4) .\)
a. Graph \(y=\cos x\) for \(0 \leq x \leq \pi\) b. Based on your graph in part (a), does \(y=\cos x\) have an inverse function if the domain is restricted to \([0, \pi] ?\) Explain your answer. c. Determine the angle in the interval \([0, \pi]\) whose cosine is \(-\frac{\sqrt{3}}{2} .\) Identify this information as a point on your graph in part (a).
Why are the trigonometric functions sometimes called circular functions?
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