There are many different formulas in chapter 10 which include sum and difference formulas, double angle formulas and half angle formulas. The easiest of these three are the sum and difference formulas for cos, sin, and tan.
The sum and difference formula for sin is sin(a +/- b)=sin(a)cos(b)+/-cos(a)sin(b)
The formula for cos is cos(a +/- b)=cos(a)cos(b) -/+ sin(a)sin(b). The sign for cos will be opposite in teh parentheses which means if it is a - b then you will end up adding the cos and sin.
the sum and difference formula for tan is tan(a +/- b)=tan(a) +/- tan(b)/1 -/+ tan(a)tan(b)
The only thing i dont understand in this section is using the formulas with fractions with different denominators.
Subscribe to:
Post Comments (Atom)
the formulas with fractions work similarly to the other problems is pretty much simple as plugging into the formula
ReplyDeleteplug in for cos/sin for alpha
but when you change cos/sin alpha into its form from the trig chart make sure you only but the trig char plug in number itself donot!! put cos/sin back in
then its just regular math from there.
Example 1: Find the exact value of sin 80 cos 130+ cos 80 sin 130
ReplyDeleteLet 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
hope that helped..