Okay so we moved on to chapter 10 last week. Its really not that hard as long as you memorize all the formulas for each section. Here are all the formulas to memorize from each section:
10-1
**Sum and difference formulas for cosine and sine:
cos (alpha + or - beta) = cos(alpha)cos(beta) - or + sin(alpha)sin(beta)
sin (alpha + or - beta) = sin(alpha)cos(beta) + or - cos(alpha)sin(beta)
**Use these formuals to rewrite a sum or difference as a product:
sin(x) + sin(y) = 2sin(x+y/2)cos(x-y/2)
sin(x) - sin(y) = 2cos(x+y/2)sin(x-y/2)
cos(x) + cos(y) = 2cos(x+y/2)cos(x-y/2)
cos(x) - cos(y) = -2sin(x+y/2)sin(x-y/2)
10-2
**Sum and difference formulas for tangent:
tan(alpha) + (beta)= tan (alpha) + tan (beta)/ 1-tan (alpha) tan (beta)
tan (alpha) - (beta)=tan (alpha) - tan (beta)/ 1+ tan (alpha) tan (beta)
10-3
**Double-angle and half-angle formulas
sin 2(alpha) = 2sin(alpha)cos(alpha)
cos 2(alpha) = cos^2(alpha)-sin^2(alpha)=1-2sin^2(alpha)=2cos^2(alpha)-1
tan 2(alpha) = 2tan(alpha)/1-tan^2(alpha)
sin(alpha/2)= +- squareroot(1-cos(alpha)/2) cos(alpha/2)= +- sqrt(1+cos(alpha)/2)
tan(alpha/2)= +- squareroot(1-cos(alpha)/1+cos(alpha))=sin(alpha)/1+cos(alpha)=
1-cos(alpha)/sin(alpha)
**Decimal- use half-angle formula to find alpha. multiply the decimal angle by 2.
I am having trouble knowing when to use what double or half angle formula. I have no clue which one to use because there are soo many similar ones. So if anyone can help me with that i would be happy! I also have trouble doing the problems when you have to make a triangle to find the angle for cos or sine. I dont understand what numbers go on the triangle, which quad the triangle goes in, and what side of the triangle the numbers go on.
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**Decimal- use half-angle formula to find alpha. multiply the decimal angle by 2.
ReplyDeleteEx: find the exact value of sin 22.5
alpha = 22.5 x 2 = 45
sin (alpha/2) = +/- sqrt 1-cos(alpha)/2
sin (45/2) = sqrt 1-cos 45/2
= sqrt 2/2 (1-sqrt2/2) all over 2
= sqrt 2 - sqrt 2/2 all over -2/1
= sqrt 2 - sqrt 2/4
= sqrt 2 - sqrt 2/2
i really that wasnt too confusing...
Use the double angle formulas when you have a decimal. But if you match the problem with the equation it makes finding the right formula alot earlier.
ReplyDeletefor the triangle the triangle goes in the first quadrant, you use SOHCAHTOA to figure out which numbers go where on the triangle, and when you need to know the missing side of the triangle you just use one of the ways we learned in the beginning of the year to solve a right triangle, or use the Pythagorean Theorem.
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