![]() ![]() 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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