Could you kindly help me with these 2 sums - Q 18 and Q21 - many, many thanks
First crosses the -axis where:So, working in degrees:
See the black graph in the attached diagram.
So let's suppose first that this graph meets where . Then:So that's one possible value of . See the yellow coloured graph.
But perhaps the diagram shows a different position of the graph, and they actually meet at a different point at which the first graph crosses the -axis; for instance, where . Then we get:This is the pink graph.
Over to you. Can you sort it out now?
For question 21: multiply top-and-bottom by :But if is obtuse, and . So . So we would have to say:, if we are given that is acute, because is then positive.
Can you see what happens for other values of ? If you're not sure, look at the graphs of and , and see whereabouts and whereabouts . And then bear in mind that has to be positive.