Something i really understand is identities. This is one of the eastiest things for me because i know it. You simplify trig equations by using both identities and algebra. Here are some of the relationships you need to look for in order to solve the equations.
Reciprocal Relationships:
cscΘ=1/sinΘ
secΘ=1/cosΘ
cotΘ=1/tanΘ
Relationships with Negatives:
sin -Θ= -sinΘ and cos -Θ= -cosΘ
csc -Θ= -cscΘ and sec -Θ= -secΘ
tan -Θ= -tanΘ and cot -Θ= -cotΘ
Pythagorean Relationships:
sin²Θ+cos²Θ=1
1+tan²Θ=sec²Θ
1+cot²Θ=csc²Θ
Cofunction Relationships:
sinΘ=cos(90°-Θ) and cosΘ=sin(90°-Θ)
tanΘ=cot(90°-Θ) and cotΘ=tan(90°-Θ)
secΘ=csc(90°-Θ) and cscΘ=sec(90°-Θ)
When you get an equation you have to first check to see if there are any identities you can use, if not you go to algebra, after that you go back to your identities and finish the problem. This is really easy you just need to memorize the relationships.
I pretty much forgot alot of stuff like solving conics...yea....and solving problems when you have to find axis of symmetry and stuff like that with the lengthy equations so i need help with that.
Subscribe to:
Post Comments (Atom)
axix of symmetry is just one formula you must remember
ReplyDeletethe formula is
X= -a/b
all you do is plug in from the given equation
remember.. in a multiple choice or short answer setting the answer must be in the form of
X=
here is an example of a parabola..
ReplyDeleteParabolas:
how to find the axis of symmetry, vertex, focus, & directrx??
1.) to find the axis of symmetry: x = -b/2a
2.) for the vertex: (-b/2a, f(-b/2a)) or use complete the square:
y = (x+a)^2 + b.....a & b are numbers and (-a,b) = vertex
3.) to find the focus: 1/4p= the coefficient of x^2 and then add p
Note:
*If opens up, add to y value from vertex, if opens down, subtract
*If opens right, add to x value to vertex, if opens left, subtract)
4.) directrix: is p units behind the vertex
Note:
*If opens up, subtract; if opens down, add from y-value of vertex.*If opens right, subtract x-value*If opens left, add x-value
Example: x^2 + 1
~vertex:
x = -b/2a
x = 0/2(1) = 0
0^2 + 1 = 1
(0,1)
~Focus:
1/4p = 1
4p = 1
p = 1/4
(0, 1 + 1/4)
(0, 5/4)
~directrix:
y = 1 - 1/4
y = 3/4
For axis of symmetry all you do is use the formula x=-a/b. a would be the coefficient of the first term, and b would be the coefficient of the second term, and you just use the equation you were given to plug this in.
ReplyDelete