109,115 108. Is the cosine function even, odd, or neither? Is its graph107 Is the sine function even, odd, or neither? Is its graph106. What is the range of the cosecant function?SECTION 6.3 Properties of the Trigonometric Functions 405What is the range of the cotangent function?109. Is the tangent function even, odd, or neither? Is its graphsymmetric? With respect to what?110. Is the cotangent function even, odd, or neither? Is its graphsymmetric? With respect to what?111. Is the secant function even, odd, or neither? Is its graphsymmetric? With respect to what?112. Is the cosecant function even, odd, or neither? Is its graphsymmetric? With respect to what?Symmetric? With respect to what?symmetric? With respect to what?Applications and ExtensionsDoblems 113-118, use the periodic and even-odd properties.120. Calculating the Time of a Trip Two oceanfront homes arelocated 8 miles apart on a straight stretch of beach, each adistance of 1 mile from a paved path that parallels the ocean.Sally can jog 8 miles per hour on the paved path, but only3 miles per hour in the sand on the beach. Because aflows directly between the two houses, it is necessary to jogin the sand to the road, continue on the path, and then jogdirectly 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 otheras a function of the angle 0 shown in the figure is113. If f(0) = sin 0 and f(a) = !find the exact value of:(a) f(-a)(b) f(a) + f(a + 27) + f(a + 4)river1cos 0 and f(a)find the exact value of:4"%3D114. If f(8)(b) f(a) + f(a + 27) + f(a – 2)(a) f(-a)15. If f(0) = tan 0 and f(a) = 2, find the exact value of:(b) f(a) + f(a + 7) + f(a + 27)(a) f(-a)116. If f(8) = cot 0 and f(a) = -3, find the exact value of:T(0) = 1 -0 <0 <3 sin 04 tan 0(a) f(-a)(b) f(a) + f(a + ™) + f(a + 47)117. If f(0) = sec 0 and f(a) = -4, find the exact value of:(b) f(a) + f(a + 27) + f(a + 47)(a) Calculate the time T for tan 0 =4'(a) f(-a)(b) Describe the path taken.118. If f(0) = csc 0 and f(a) = 2, find the exact value of:(c) Explain why 0 must be larger than 14°.(a) f(-a)119. Calculating the Time of a Trip From a parking lot, youwant to walk to a house on the beach. The house is located1500 feet down a paved path that parallels the ocean, whichis 500 feet away. See the figure. Along the path you can walk300 feet per minute, but in the sand on the beach you canonly walk 100 feet per minute.The time T to get from the parking lot to the beachhouse expressed as a function of the angle 0 shown in thefigure is(b) f(a) + f(a + 27) + f(a + 4 )Осean4 mi4 mi -Beach1 miPaved path ----RiverT(0): 50 < 0 <3 tan 0sin 0121. Predator Population In predator-prey relationships, th.populations of the predator and prey are often cyclical. Ia conservation area, rangers monitor the red fox populaticand have determined that the population can be modeledthe functionCalculate the time Tif you walk directly from the parking lotto the house.500(Hint: tan e =1500OceanP(t) = 40 cos-+ 110 ba1RIwhere t is the number of monthsfrom the time monitoring began.Use the model to estimate theBeach500 ftPaved pathpopulation of red foxes inthe conservation area after10 months, 20 months, and30 months.Forest1500 ftParking lot

We will use the simple definition of odd function and even function to show tangent function is odd…

SECTION 6.3 Properties of the Trigonometric Functions 405 104. What is the range of the cotangent function? 105. What is the range of the secant function? 106. What is the range of the cosecant function? 107. Is the sine function even, odd, or neither? Is its graph symmetric? With respect to what? 108. Is the cosine function even, odd, or neither? Is its graph 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? symmetric? With respect to what? 112. Is the cosecant function even, odd, or neither? Is its graph symmetric? With respect to what? Applications and Extensions In Problems 113–118, use the periodic and even-odd properties. 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 = sin 0 and f(a) 113. If f(0) find the exact value of: 3' (a) f(-a) (b) f(a) + f(a + 27) + f(a + 47) 1 find the exact value of: = cos 0 and f(a) 114. If f(0) (a) f(-a) (b) f(a) + f(a + 27) + f(a - 27) = tan 0 and f(a) = 2, find the exact value of: 115. If f(0) (a) f(-a) 16. If f(0) = cot 0 and f(a) = -3, find the exact value of: (b) f(a) + f(a + T) + f(a + 27) 2. 2 T(0) = 1 + 3 sin 0 4 tan 0

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...