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Explain the relationship(s) among angle measure in degrees, angle measure in radians, and arc length. Answer: Find the exact value of each of the following. In each case, show your work and explain the steps you take to find the value. sin (a) tan 13 4 sec 11 3 Answer: 17  6 Consider the right triangle ABC given below: (a) Find the length of side b to two decimal places. (5 points) (b) Find the length of side a to two decimal places in three different ways. (5 points) Answer: Consider the right triangle ABC given below: (a) What is the length of the hypotenuse of triangle ABC? What is the length of the shorter leg of triangle ABC? What is the length of the longer leg of triangle ABC? Answer: Give an example of a real number t for which cos t is positive and sin t is negative. Answer: If the arc length shown is 15 feet, find  to the nearest hundredth of a degree. Answer: Sam used his calculator to find cos1.75 . He wrote down cos1.75  .999 . How could Sam recognize that his answer is incorrect? Answer: Sarah used her calculator to find sin125 . She wrote down sin125  .57 . How could Sarah recognize that her answer is incorrect? Answer: ...
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vmohanakumar
School: Cornell University

Attached. Let me know if you have any questions.

Explain the relationship(s) among angle measure in degrees, angle measure in radians, and arc length.
Answer:
One degree measure of an angle is defined as 1/360 of a full revolution in magnitude. Half revolution is
180 degrees and a right angle is one fourth of a revolution and its measure is 90 degrees. One radian
measure is defined as the angle formed by an arc of a circle of arc length same as its radius. Since one
complete circle with radius r has a circumference of 2πr, one revolution forms an angle of 2π radians.
Hence if the angle measure is in radians, we can find the arc length by simply multiplying the radius by
the angle measure. Similarly to find the angle in radians, divide the arc length by the radius.
The relationship between the angle in radian measure and arc length is S = rΘ, where S is the arc length,
r is the radius and Θ is the angle in radians.
The relationship between an angle in radian measure and degree measure is
One compete revolution = 3600 = 2π radians.
Hence 1 radian = (360/2π)0 = (180/π)0
And 10 = (π/180) radians.

Find the exact value of each of the following. In each case, show your work and explain the steps you
take to find the value.
sin

(a...

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