5. Let h(x)=3cosx and let k(x)=1+5cosx . What are all values of x in the xy-plane, 0leqslant xleqslant 2pi for which h(x)leqslant k(x)

To figure out where , we need to solve the inequality.Let's start by setting , or . Solving this for gives us .The inequality means that the cosine curve for is below or equal to .Next, by examining the nature of the cosine function, which fluctuates between -1 and 1 regardless of the scalar multiply (the 3 and the 5 here), both curves oscillate equally, but will always be 1 unit above.The points of intersection occur when . The solutions to this lie in the given interval, are and from the nature of cosine function. However the feeling inequality points to so consider values less than these points or in between of such occurrences.Thus, in the interval , for interval set given by:Time for cosx = 1/2: = 1/cos^-1[ 1/2], and = (2pi — ). Always less than equalTIme for g(x) > h(x) only twice a integral hemisphere of cosine so it is present only between these times above