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trigonometry2 revision sheet

By Craig Russell,2014-07-05 09:52
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trigonometry2 revision sheet

    Addition formulae Special angles Double angle formulae (learn!)

    sin22sincosAAA

    2232,,,1sin()sincoscossinABABAB(?( cos2cossinAAA?;sin();sin();sin()??? 624232 22 ?;?;12sin2cos1AAcos()coscossinsinABABAB(? 32,,,1cos();cos();cos()??? 6242322tanA tan2A2 1tanAtantanAB(,,,1 tan()AB(?tan();tan()1;tan()3??? Also learn these rearrangements: 64331tantanAB21cos(1cos2)AA?; 2

    21sin(1cos2)AA?; 2

     Solving equations: Solving equation example:

    2sincot0xx;?02,,x for Solve sinxk To solve equations , get one value cosxkcosx Solution: (def’n of cotx) 2sin0x;?sinxtanxk~2nd2sincos0xx;? (multiply by sinx) from your calculator and then the 2 value is 22sincos1xx;?We now use the relationshipto ;;xxor 180forsinget equation in terms of cosx only. 22or360forcos;;xx. 2(1cos)cos0;;?xx 22coscos20xx;;? ;;xxor180fortan~Using the quadratic formula: Further values can be obtained by adding (or cos0.7808(or1.2808)x?; taking away) multiples of 2π or 360?.

    So, x = 0.675 or x = 2π 0.675 = 5.61.

    abcossin!!;Step 3: Find R (by eliminating α). We can now see that the maximum and Expressions for

     2222222R(cossin)2313;?;??? + (2): (1)13 minimum values of 2cosx 3sinx will be Example: Write 2cosx 3sinx in the form 213RR?;?1313 and respectively. Rxcos(); .

    Rxcos();Step 1: Write out the expansion of : The maximum value occurs when Step 4: Find α (by eliminating R):

    cos(0.983)1x;? tan1.50.983???;?RxRxRxcos()coscossinsin;?;???(2)/(1):

     So: x + 0.983 = 0 or Step 2: Compare expressions: i.e. x = -0.983 or 5.30. 13cos(0.983)x;Step 5: So, 2cosx 3sinx = RRcos2(1)andsin3(2)????

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