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PreCalc Final Review

for Thaemert's 1st Semester Final

QuestionAnswer
Odd functions are symmetrical about the origin. Ex: (2,4) (3,1) (-2,-4) (-3,-1)
Even functions are symmetrical about the y-axis. Ex: (2,4) (3,1) (-2,4) (-3,1)
How to determine if a function is odd, even, or neither. PLUG IN... -X or -1 for X Odd is negated, Even is exact same
When given real world function like: D(p)=1200-200(p) and asked to find the D-1, plug in the number they give you into D(p)
f(0)= y intercept
f(x)=0= asymptote
F is less than or equal to. Remember, it is always left to right
He doesn't want you to solve for e
On domain and range problems, the y-int is included in the range. Don't graph! Ex:y=2x-9 [-9,inf)
A sin wave has a domain, range, and period of... D:(-inf,inf) R:[-1,1] P:2pi
A cos wave has a domain, range, and period of... D:(-inf,inf) R:[-1,1] P:2pi
A tan wave has a domain, range, and period of... D:(all real numbers except odd multiples of pi/2 R:(-inf,inf) P:pi
A csc wave has a domain, range, and period of... D:(all real numbers except multiples of pi) R:(-inf,-1]U[1,inf) P:2pi
A sec wave has a domain, range, and period of... D:(all real numbers except odd multiples of pi/2) R:(-inf,-1]U[1,inf) P:2pi
A cot wave has a domain, range, and period of... D:(all real numbers except multiples of pi) R:(-inf,inf) P:pi
For problems where it asks to find domain and range, use parentheses. Ex: 3x^3/2x-9 (3x^3)/(2x-9)
To convert degrees to radians manually... degree/1 X pi/180, simplify
To convert radians to degrees manually... radian X 180/pi, simplify
For trig functions, always draw the triangle with cross and remember SOHCAHTOA
For problems like sin(cos-1(1/5)), draw the triangle. The 1 would be adjacent over the 5 hypotenuse
He doesn't care if your radicals are simplified on trig function problems
If you see a problem like this: 1^2+x^2, it becomes \/1-x^2
Make sure you are degrees and radians for the right problems!
law of sines sinA/a=sinB/b=sinC/c
law of cosines a^2=b^2+c^2-2bccosA
Don't forget that if you have 2 angles, you find the third through 180-a-b=c
theta=inverse trig function(corresponding sides) Ex: theta=tan-1(opposite/adjacent)
When trying to find the period, midline, amplitude, h. shift, and v. shift.... y=Acos(B(x-h))+k
Remember to note the midline as... y=m
If a h. shift does occur, remember it is always in the opposite direction and PUT IT OVER THE B VALUE Ex: (3x-pi) HS=pi/3
Period should be noted as T
When faced with a problem with two trig functions Ex: 2sincos+cos=0, find the GCF or FOIL. Once fully factored, set =0 and solve for theta, not trig function Ex: sinx=1 X=pi/2
Expand all composite functions, foil, then distribute. Ex: 2(5x-7)^2 2(5x-7)(5x-7) 2(25x^2+70x+49) 50x^2+140x+98)
sin^2+cos^2=1
A function is a relation that is a one-to-one mapping of one element of the domain to exactly one and only one element of the range
When finding domain, set denominator =0
Remember that a negative quadratic is upside down
tangent of pi/6 radical3/3
tangent of pi/3 radical 3
When finding a side length with angle, side and right triangle, use this formula... funX=(x/side) or (side/x) depending on what trig function
On problems where he asks you to give the solutions to a multiple function prob Ex: 2sin-cos, always check what interval Ex: [0,2pi) 0 CAN BE A SOLUTION TO THETA
Use inverse trig function when trying to solve for theta, but the number he gives you is irregular. Then, subtract from 2pi.... Ex: 2/3 cos-1(2/3)=.841 2pi-.841=5.442
When proving identities, find a common denominator
remember when solving sum to product, there is no such thing as negative theta so change it to positive
when solving sum and difference problems, remember to multiply radicals and the denominators
Created by: whitltre000