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This 3 page Class Notes was uploaded by Aileen Davis on Tuesday October 20, 2015. The Class Notes belongs to MATH0008 at Sierra College taught by RebeccaKyler in Fall. Since its upload, it has received 144 views. For similar materials see /class/225371/math0008-sierra-college in Mathematics (M) at Sierra College.
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Date Created: 10/20/15
Math 8 25 UniT Circle Approach Properties of The Trigonomefric Functions Consider a circle given by The equaTion x2 y2 1 called a uniT circle Y On a uniT circle The measure of a cenTraI angle 9 and The engTh of iTs arc 7 can be represenTed by The same real number Thus t So sint9sint Definifion of The Trig Funcfions of Real Numbers These should look familiar sintb csctlb 0 b 1 costa sect a 0 Pabcosts1nt a b a tant a 0 c0tt b 0 a b MFill in The UniT Circle HandouT EX Find The exacf value of each funcfion STeps Make a skeTch deTermine which quadranT The Terminal side of The angle lies and Then use The reference angle To deTermine The value a sin b sec 4 3 Domain and Range of The TrigonomeTric FuncTions FuncTion Domain Range sin 6 All real numbers 00 00 1 S Sin 6 S1 0056 All real numbers 00 00 1 S 0056 S1 77 a tan 6 00 00 excepT odd inTeger mulTiples of E 0quot 90 00 lt tan 6 lt 00 0506 00 00excepT odd inTeger mulTiples of 7239 0quot 180 0506 S 1 0quot 0506 21 77 o 5606 00 00excepT odd inTeger mulTiples of E 0quot 90 5606 S 1 0quot 606 21 cot6 00 00excepT odd inTeger muITipIes of 7239 or 180 00 lt cot6 lt oo Periodic ProperTies A funcTion fis called periodic if There is a posiTive number 0 such ThaT whenever 6 is in The domain of f so is 6 17 and f6 p f6 The smallesT such number p is called The fundamenTal period of f Sine cosine and cosecanT and secanT all have a period of 27239 TangenT and coTangenT have a period of 7239 EX Use The facT ThaT The Trig funcTions are periodic To find The exacT value of a cos420 b sin a Use Even Odd ProperTies To Find The ExacT Values of The TrigonomeTric FuncTions Recall TesTs for evenodd polynomial funcTions 2 y EvenOdd ProperTies sin 6 sin6 tan 6 tan6 csc 6 csc6 cot 6 cot6 cos 6 0056 sec 6 5606 EX Use The Even Odd ProperTies To deTermine wheTher The given funcTion is even odd or neiTher Is iTs graph symmeTric WiTh respecT To whaT a fx 2cosx b fx251nx EX Use The periodic and even odd properTies for The following If cosx and fa i find The exacT value of a f a b fafa27rfa 27r