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