Homework Assignment 3 – The Travels of a T-Shirt in the Global Economy Objectives of this Assignment – The overarching goal of this activity is to assist you in recognizing the structure, dynamics, and complexities comprising the global marketplace. Side, so pick whichever seems like an easier starting point.Įxample 1: Prove that sec2x + cosec2x = sec2x cosecax When proving identities, you must start from one side and work your way towards the other side.
As with most of mathematics, the most useful tool here is practice. With these functions and the above identities.
Using reciprocal functions and identities is being tested, so the most useful thing you can do is properly familiarise yourself Your ability to manipulate trigonometric expressions There is no trick or standard procedure to be used for these questions. Below are the graphs of the reciprocal functions You need to be able to sketch the reciprocal trigonometric functions as well as any transformations, Reflecting y = cosx in the line y = x using the domain 0 < x < t gives us its inverse function, arccosx: You can use the definitions and identities we have covered so far to simplify and prove expressions involving the reciprocal Simplifying expressions and proving identities The negative power has a different meaning when used with trigonometric functions. Since division by zero is undefined, we have that these functions are undefined when the denominatorsĬareful: It is not true that: secx = (cosx)-1, cosecx = (sinx)-1, cotx = (tamx)-1 (undefined for values of x for which tanx
(undefined for values of x for which sinx = 0) Sxs gives us its inverse function, arcsinx: (undefined for values of x for which cosx = :0) This chapter introduces three more trigonometric functions, known as the reciprocal trigonometric Recall from Pure Year 1, that sin²x + cos²x = 1 Which we can sketch by reflecting the sinx, cosx and tanx graphs in the line y This allows us to define the inverse functions, We restrict the domains, we can turn them into one-to-one functions.
The trigonometric functions aren't one-to-one by definition, but if Previously, you have met three trigonometric functions sinx,cosx and tanx.Ī function only has an inverse if it is one-to-one.
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