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# PreCalc Final Review

### for Thaemert's 1st Semester Final

Question | Answer |
---|---|

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 |