Pre calc 5B Flashcards
Triangle ABC has side lengths of 18 (across from C) 20 (across from A) and 30 (across from B)
a. Which angle should you find first
b. Find angle B
c. Find angle A
d. Find angle C
a. the biggest angle which would be across from the biggest side so B
b. use Law of Cosines
(b^2 = a^2 + c^2 -2bc times cos B) -> letters are interchangable
then rearrange to get
B = cos^-1 ( (b^2 - a^2 - c^2)/(-2)(b)(a))
Plug in the numbers to get 104.149 degrees
c. to find A use Law of Sines
Sin A/20 = SinB/30 -> A = sin^-1 (20sinB/30)
A= 40.273 degrees
c. to find C use the fact that all three angles of a triangle add up to 180 -> 180-A-B =35.577 degrees
What are the area formulas for a triangle
What is s?
(1/2)abSinC
square root of s(s-a)(s-b)(s-c)
s = (a+b+c)/2
For y=sinx what is the
a. Amplitude
b. Period
c. Domain
d. Range
e. Asymptotes
f. Zeroes
a. 1
b. 2pi
c. all real numbers
d.
-1 is less then or equal to y is less then or equal to 1
e. none
f. x = pik
REMEMBER THAT K IS AN INTEGER WHICH IS SHOWN BY
KE WEIRD Z AND 7
For y=cosx what is the
a. Amplitude
b. Period
c. Domain
d. Range
e. Asymptotes
f. Zeroes
a. 1
b. 2pi
c. all real numbers
d.
-1 is less then or equal to y is less then or equal to 1
e. none
f. x = pi/2 + piK
REMEMBER THAT K IS AN INTEGER WHICH IS SHOWN BY
KE WEIRD Z AND 7
For y=tanx what is the
a. Amplitude
b. Period
c. Domain
d. Range
e. Asymptotes
f. Zeroes
a. none
b. pi
c. x cannot = pi/2 + piK
d. all real numbers
e. x = pi/2 + piK
f. x = piK
REMEMBER THAT K IS AN INTEGER WHICH IS SHOWN BY
KE WEIRD Z AND 7
How would you graph y = sinx
actually graph on paper and describe
4 from origin is pi 4 from pi is 2pi same on neagtive direction
at -2pi,-pi, 0, pi, and 2pi the line is at y - 0
at the half way point between origin and pi the line is at 1
at the half way point between pi and 2pi the line is at -1
at the half way point between the origin and -pi the line is at -1
at the half way point between -pi and -2pi the line is at 1
How would you graph y = cosx
actually graph on paper and describe
4 from origin is pi four from pi is 2pi same in negative direction
at 0 y = 1 at pi y = -1 at 2pi y = 1 at -pi y - -1 at -2pi y = 1
half way between origin and pi is y=0 same half way between pi and 2pi, origin and -pi, and -pi and -2pi
How would you graph y = tanx
actually graph on paper and describe
first two asymptotes are 2 from origin in the positive and negative directions (the asymptotes keep goin 4 apart infinitely after that)
in the middle of each asymptote there is a line, draw it by using the middle as the origin where on dot is then the other two dots are one up and one over to the right along with one down and one over to the left
How do you find
a. amplitude
b. Period
Given aSinbx or aCosbx
a. absolute value of a
b. 2pi/absolute value of b
y= -2sin4x
a. amplitude
b. period
c. Graph
a. 2
b. pi/2
c. because the period is pi/2 have 4 out from origin be pi/2
because the amp is two go up or down 2
You go down first when graphing the right side because its negative, up when going left
You have to go a full rotation between origin and pi/2 (because a period is a full rotation and the period is pi/2) so it has to go up and down which is why one in is -2 and one further is 0 then one further is 2 and finally pi/2 is 0 (in the right direction)
An angle theta is in standard position a point on the terminal angle is (-4,7)
find
a. Sin(theta) Csc(theta)
b. Cos(theta) Sec(theta)
c. Tan(theta) Cot(theta)
adjacent is -4 opposite is 7
find hyp through pythagory theorem
hyp = square root of 65
a. 7(squareroot of 65)/65, squarerootof 65/7
b. -4(squarerootof 65)/65, -squarerootof 65/4
c. -7/4, -4/7
