Inverse Trigonometric functions Questions

12. [4/7 Points]
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LARCALCET7 5.4.050.MI.SA.
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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any
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Math

Inverse Trigonometric functions

12. [4/7 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 5.4.050.MI.SA. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. TT f(x) = cos(x), [:) 3 Step 1 Recall that the Mean Value Theorem is stated as follows. If fis continuous on the closed interval [a, b], then there exists a number c in the closed interval [a, b] such b that * S** f(x) dx = f(c)(b - a). In terms of area, this means there is a rectangle with side lengths f(c) and (b - a) that has the same area as found by f(x) dx. We are given the function f(x) = cos(x) and the interval 3 3 The function f(x) is is continuous on the given interval. Therefore, we must find the value of c in - [- that makes the following equation true. 3 3 2/3 L cos(x) dx = cos(c)( /3 3 cols Step 2 We will first evaluate the given integral. #/3 1/3 (cos(x)) dx = 1/3 (sin(x)] - 1/3 NT = sin - in(-) w = Step 3 We have evaluated the given definite integral. Substitute this value on the left side of the equation and then solve for f(x) = cos(c) in the Mean Value Theorem. 1/3 (cos(x)) dx = cos(c) #/3 * = cos(1)-(-) V3 - costil-(-3) V3 = cos(c)( V3 27 3 0.5973 3V3 27 = cos(C) Step 4 Solve for c. Use inverse trigonometric functions to find the value of c guaranteed by the Mean Value Theorem for the function over the given interval. (Round your answers to four decimal places. Enter your answer as a comma-separated list.) 313 cos(C) 21 = arccos(cos(c)) = arccos cos(325) C = 89.1729,270.8271 X Submit Skip (you cannot be

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