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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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