Pre Calc s2 final

Question 1

How do you solve a problem like cos(105) = ___?

Answer 1

105 -> 45+60
so use the equation in the trig table to get cos45(cos60) - sin45(sin60)
answer is (square root of 2 - square root of 6)/4

Question 2

How do you solve a problem like
If cosx = 2(squarerootof5) / 5
and 3pi/2 < x < 2pi
then find Cos2x and Sin2x

Answer 2

because of the 3pi/2 and 2pi we know this is in quadrant 4
Use pythagorean theorem to find all three sides
Then use the given equations to solve

Question 3

How do you solve a problem like
a. cosx = -squareroot3 / 2
b. cscx = -2

Answer 3

a. from the negative we know its in the 2nd and 3rd quadrant
and that the corresponding angle is pi/6
so the answer is 5pi/6, 7pi/6 + 2pik kEZ
b. change to sin (which is -1/2)
its negative so we know the quadrant is 3 and 4
and that the corresponding angle is pi/6
which means x = 7pi/6, 11pi/6 + 2pik kEZ

Question 4

what is this angle in degree minute second (DMS) form?
36.875degrees

Answer 4

36 is the thing that remains degrees
you then take the 0.875 and multiply it by 60(or60/1) which gives you 52.5
you then take the 0.5 and multiply it by 60(or60/1) which gives you 30
this all together gives the answer of 36 degrees 52^I 30 ^II

Question 5

What is this angle measure in decimal degree form?
-98degrees 12^I 48^II

Answer 5

-98 is the thing that remains as degrees
you then take the 12 and multiply it by 1/60 which gives you 0.2
then you take the 48 and multiply it by 1/3600 which gives you 0.0133333
all together this gives you the answer of -98.213g

Question 6

solve
a. arccos ( square root of 3/2)
b. arcsin (-1)
c. arctan(square root of 3)

Answer 6

a. = pi/6
b. = -pi/2
c. = pi/3

Question 7

solve arctan(tan 5pi/6)

Answer 7

since this is not in range we have to solve it the harder way
First find out what quadrant this angle would be in do is be converting it to degrees. (divide 180 by 6 then multiply that number by 5) or just use the unit circle
the quadrant tells you if its positive or negative
Then you know that the answer is negative pi/6

Question 8

solve tan(arccos squarerootof 2/2)

Answer 8

First think of which triangle these numbers correspond to the answer is the 45 45 90 triangle
so you know that the (arccos(squarerootof 2/2)) = pi/4
then you solve tan(pi/4) which means you find the tangent of 45 degrees which gives you 1

Question 9

what do the different things mean on a sigma(weird rectangle)
a. number on top
b. number on bottom
c. numbers to the right

Answer 9

a. the number on top is the term number so if its five that means you stop calculating when n = 5
b. the number on the bottom is the first number (number you start calculating with)
c. the big numbers to the right is the formula (what you plug the numbers in to

Question 10

For ellipses:
a. What is the major axis, and how long is it
b. What is the minor axis, and how long is it
c. what are the vertices, and how far are they from the center
d. what are the co-vertices, and how far are they from the center
e. how far are the foci from the center

Answer 10

a. Longer axis of symmetry, 2a
b. shorter axis of symmetry, 2b
c. end points of the major axis, a
d. end points of the minor axis, b
e. c

Question 11

For hyperbolas:
a. the center is the _____ of the foci
b. The vertices are ____ from the center
c. the co-vertices are _____ from the center
d. what is the transverse axis, and how long is it
e. what is the conjugate axis, and how long is it
f. the foci are _____ from the center

Answer 11

a. midpoint
b. a
c. b
d. it connects the vertices and is 2a long
e. it connects the co-vertices and is 2b long
f. c