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109. Is the tangent function even, odd, or neither? Is its graph symmetric? With respect to what?

109. Is the tangent function even, odd, or neither? Is its graph symmetric? With respect to what?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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109,115,121
108 Is the cosine function even, odd, or neither? Is its graph 115. If f(0) = tan 0 and f(a) = 2, find the exact value of: In Problems 113-118, use the periodic and even-odd properties. 107. Is the sine function even, odd, or neither? Is its graph SECTION 6.3 Properties of the Trigonometric Functions 405 109. Is the tangent function even, odd, or neither? Is its graph symmetric? With respect to what? 110. Is the cotangent function even, odd, or neither? Is its graph symmetric? With respect to what? 111. Is the secant function even, odd, or neither? Is its graph symmetric? With respect to what? aymmetric? With respect to what? 112. Is the cosecant function even, odd, or neither? Is its graph symmetric? With respect to what? ymmetric? With respect to what? 120. Calculating the Time of a Trip Two oceanfront homes are located 8 miles apart on a straight stretch of beach, each a distance of 1 mile from a paved path that parallels the ocean. Sally can jog 8 miles per hour on the paved path, but only 3 miles per hour in the sand on the beach. Because a river flows directly between the two houses, it is necessary to jog in the sand to the road, continue on the path, and then jog directly back in the sand to get from one house to the other. See the figure. The time T to get from one house to the other as a function of the angle 0 shown in the figure is find the exact value of: 113. If f(0) = sin 0 and f(a) = ! (b) f(a) + f(a + 27) + f(a + 47) (a) f(-a) 1 find the exact value of: U4. IE f(0) = cos 0 and f(a) = (b) f(a) + f(a + 27) + f(a – 27) (a) f(-a) (b) f(a) + f(a + 7) + f(a + 27) (a) f(-a) H6 If f(0) = cot 0 and f(a) = -3, find the exact value of: 2. T(0) = 1 + 0 < 0 < isioa 3 sin 0 4 tan 0 (b) f(a) + f(a + 7) + f(a + 4T) (a) f(-a) U7. Jf f(0) = sec 0 and f(a) = -4, find the exact value of: 1 (a) Calculate the time T for tan 0 = (b) f(a) + f(a + 27) + f(a + 47) (a) f(-a) U8 If f(0) = csc 0 and f(a) = 2, find the exact value of: (b) Describe the path taken. (c) Explain why 0 must be larger than 14°. (b) f(a) + f(a + 27) + f(a + 47) (a) f(-a) 119. Calculating the Time of a Trip From a parking lot, you want to walk to a house on the beach. The house is located 1500 feet down a paved path that parallels the ocean, which is 500 feet away. See the figure. Along the path you can walk 300 feet per minute, but in the sand on the beach you can only walk 100 feet per minute. The time T to get from the parking lot to the beach house expressed as a function of the ie 9 shown in the figure is Ocean 4 mi + 4 mi Beach 1 mi Paved path River 5 T(0) = 5 – 3 tan 0 sin 0 Calculate the time Tif you walk directly from the parking lot to the house. 121. Predator Population In predator-prey relationships, the populations of the predator and prey are often cyclical. In a conservation area, rangers monitor the red fox population and have determined that the population can be modeled by 500 Hint: tan e = 1500 the function P(t) = 40 cos + 110 bat JR Ocean where t is the number of months from the time monitoring began. Use the model to estimate the population of red foxes in the conservation area after Beach 500 ft Paved path Forest 1500 ft Parking lot 10 months, 20 months, and 30 months.
Transcribed Image Text:108 Is the cosine function even, odd, or neither? Is its graph 115. If f(0) = tan 0 and f(a) = 2, find the exact value of: In Problems 113-118, use the periodic and even-odd properties. 107. Is the sine function even, odd, or neither? Is its graph SECTION 6.3 Properties of the Trigonometric Functions 405 109. Is the tangent function even, odd, or neither? Is its graph symmetric? With respect to what? 110. Is the cotangent function even, odd, or neither? Is its graph symmetric? With respect to what? 111. Is the secant function even, odd, or neither? Is its graph symmetric? With respect to what? aymmetric? With respect to what? 112. Is the cosecant function even, odd, or neither? Is its graph symmetric? With respect to what? ymmetric? With respect to what? 120. Calculating the Time of a Trip Two oceanfront homes are located 8 miles apart on a straight stretch of beach, each a distance of 1 mile from a paved path that parallels the ocean. Sally can jog 8 miles per hour on the paved path, but only 3 miles per hour in the sand on the beach. Because a river flows directly between the two houses, it is necessary to jog in the sand to the road, continue on the path, and then jog directly back in the sand to get from one house to the other. See the figure. The time T to get from one house to the other as a function of the angle 0 shown in the figure is find the exact value of: 113. If f(0) = sin 0 and f(a) = ! (b) f(a) + f(a + 27) + f(a + 47) (a) f(-a) 1 find the exact value of: U4. IE f(0) = cos 0 and f(a) = (b) f(a) + f(a + 27) + f(a – 27) (a) f(-a) (b) f(a) + f(a + 7) + f(a + 27) (a) f(-a) H6 If f(0) = cot 0 and f(a) = -3, find the exact value of: 2. T(0) = 1 + 0 < 0 < isioa 3 sin 0 4 tan 0 (b) f(a) + f(a + 7) + f(a + 4T) (a) f(-a) U7. Jf f(0) = sec 0 and f(a) = -4, find the exact value of: 1 (a) Calculate the time T for tan 0 = (b) f(a) + f(a + 27) + f(a + 47) (a) f(-a) U8 If f(0) = csc 0 and f(a) = 2, find the exact value of: (b) Describe the path taken. (c) Explain why 0 must be larger than 14°. (b) f(a) + f(a + 27) + f(a + 47) (a) f(-a) 119. Calculating the Time of a Trip From a parking lot, you want to walk to a house on the beach. The house is located 1500 feet down a paved path that parallels the ocean, which is 500 feet away. See the figure. Along the path you can walk 300 feet per minute, but in the sand on the beach you can only walk 100 feet per minute. The time T to get from the parking lot to the beach house expressed as a function of the ie 9 shown in the figure is Ocean 4 mi + 4 mi Beach 1 mi Paved path River 5 T(0) = 5 – 3 tan 0 sin 0 Calculate the time Tif you walk directly from the parking lot to the house. 121. Predator Population In predator-prey relationships, the populations of the predator and prey are often cyclical. In a conservation area, rangers monitor the red fox population and have determined that the population can be modeled by 500 Hint: tan e = 1500 the function P(t) = 40 cos + 110 bat JR Ocean where t is the number of months from the time monitoring began. Use the model to estimate the population of red foxes in the conservation area after Beach 500 ft Paved path Forest 1500 ft Parking lot 10 months, 20 months, and 30 months.
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