The Inverse Cosine Function
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Transcript of The Inverse Cosine Function
The Inverse Cosine FunctionLesson 5.3
Reminder y = cos x
Reminder y = cos x
Remember y = sin x
Remember y = sin x
Remember y = tan xLorem
y = tan-1 xLorem
To summarize
DomainRangeSin-1x-1 x 1-/2 y /2Cos-1x-1 x 10 y Tan-1xSet of all reals-/2 y /2
Example 1The top of the crossbar in each goal post in high school football is 10 feet off the ground. Express the measure of the angle of elevation from a point halfway between the sidelines to the top of the crossbar as a function of the distance d in yards from a point directly below the middle of the crossbar. 10 feetcrossbarPoint on fieldd
Example 2If x < 0 and y > 0, write cos (sin-1(x/y)) in terms of x and y.2nd quadrant cos is negativexy?x2 + ?2 = y2?2 = y2 x2
Example 3Solve sin x = -.8245x = arcsin(-.8245)x = -55.54 + 360k 2.35.5378 + 360kOR -.9693 + 2k, -2.1722+2k
HomeworkPages 4722, 14 - 17