ok we had like only three days this week..so we pretty much just reviewed for the test..here's some examples of the stuff we gonna have to know..
Example 1: Find the exact value of sin 80 cos 130+ cos 80 sin 130
Let alpha = 80 and beta = 130 then sin 80 cos 130 + cos 80sin 130 = sin alpha cos beta + cos alpha sin b
= sin (alpha + beta)
= sin (80+130)
= sin (210)
= sin (180 + 30)
= - sin 30
= -1/2
Example 2: Find the exact value of
cos^215 - sin^215 = cos(2alpha)
= cos(30)
= sqrt 3/2
Example 3: cos 15
alpha = 45, beta = 30
cos (alpha - beta) = cos 45 cos30 + sin45 sin 30
cos (45 - 30) = (√(2/2) (√(3/2) + (√(2/2) (1/2)
= √(√6 + √2)/all over 4
Example 4: (1 + cot^2) (1 - cos 2x)
(csc^2x) (1-cos2x)
(csc^2x) (1-(1 - 2sin^2x)
(1/sin^2x) (2sin^2x)
= 2
Example 4: 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 6: Find the exact value of tan15 +tan30/1-tan15 (tan30)
= tan(15 + 30)
= tan(45)
= 1
alrighty then, i hope that's enough examples to help someone out..ok what i need help with is the problems you gotta make a triangle and some how suppose to figure it out..so thanks to whoever can help me out with that..
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I had this exact same problem but Mrs. Robinson explained it to me so hopefully I can help. Okay so if you have a problem like...
ReplyDeleteSin 2A= 2 SinA CosA SinA=5/13
so you replace SinA with 5/13
Sin 2A= 2(5/13)CosA
To find CosA, you have to make a triangle using 5,12,13 because it is a perfect triangle
So you make your triangle and you know that Cos is x/r.....
So your answer for CosA would be (12/13)
Plug into the egn.
Sin 2A= 2(5/13)(12/13)= plug into your calculator and thats your answer
I hope this helps.... its hard to explain through a comment so ill explain it at school if you need me too!!!
When you face a problem like this, makes sure you know the trig functions. sin(a)=y/r, cos(a)=x/r, tan(a)=y/x, csc(a)=r/y, sec(a)=r/x, cot(a)=x/y. If you know these and you can set the triangle up then it is fairly easy.
ReplyDeleteAll you need to do is use Trig functions. to finish the triangle you find the missing length and then plug in the answer to either sin or cos depending on which one you needed to find.
ReplyDelete