alrighty so we had a short week of school which was great!! We just reviewed for our big chapter 10 test that is tuesday so ill put some examples of problems we need to study.
Ex: Find the exact value of 2sin15cos15
=sin2a
=sin2(15)
=sin30
=1/2
Ex: Find the exact value of sin 15
alpha=45 beta=30
sin(45-30)=sin 45 cos 30- cos 45 sin 30
sin 15= (squareroot of 2/2) (squareroot of 3/2)-(squareroot of 2/2)(1/2)
sin 15= squareroot of 6 - squareroot of 2/4
Ex: Find the exact value of cos 75
alpha = 45 beta = 30
cos(a + b) = cos(a)cos(b)-sin(a)sin(b)
cos 75 = (squareroot of 2/2)(squareroot of 3/2) - (squareroot of 2/2)(1/2)
cos 75 = (squareroot of 6 - squareroot of 2)/4
okay so study all the formulas and it should be pretty easy if you know the formulas, trig chart, and unit circle. GOODLUCK everyone!!!
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Here are some examples:
ReplyDeleteExample 1: Find the exact value of sin22.5
alpha=2(22.5)
alpha=45
**if you are given an angle with a decimal you use the half-angle formula. To find alpha, you multiply by two.
Example 5: Sum Formula for Cosine
cos 75 cos 15 + sin 75 sin 15
=cos (75-15) = cos 60 = 1/2
Example 2: Find the exact value of tan15 +tan30/1-tan15 (tan30)
= tan(15 + 30)
= tan(45)
= 1