Semester 1 Final

Question 1

What are cofunctions

Answer 1

Sin/Cos Tan/Cot Sec/Csc

Question 2

What does coterminal mean

Answer 2

terminal sides coincide

Question 3

Supplement =
Complement =

Answer 3

Supplement = 180
Complement = 90

Question 4

How can you convert from radians to degrees

Answer 4

R/D=π/180

Question 5

Sine

Answer 5

Sin=y/r=Opp/Hyp

Question 6

y=sin(x)

Answer 6

amplitude- 1
domain- all real #
range- [-1,1]
period- 2π

Question 7

y=cos(x)

Answer 7

amplitude-1
domain- all real #
range- [-1,1]
period-2π

Question 8

y=tan(x)

Answer 8

amplitude-1
domain-all real #, x≠π/2+πn
range- all real #
period- π

Question 9

y=csc(x)

Answer 9

amplitude-1
domain- all real #,x ≠πn
range- (-∞,-1]u[1,∞)
period- 2π

Question 10

y=sec(x)

Answer 10

amplitude-1
domain- all real #, x≠π/2+πn
range- (-∞,-1)u(1,∞)
period- 2π

Question 11

y=cot(x)

Answer 11

amplitude-1
domain- all real #, x≠πn
range- all real #
period- π

Question 12

y=asinb(x-h)+k

Answer 12

amplitude- absolute value of a
period- 2π/b or π/b
phase shift- -h
verticle displacement- k
reflection- -a is x-axis reflection

Question 13

inverse vs reciprocal

Answer 13

inverse = switching x&y
reciprocal = 1/x or 1/y

Question 14

even functions

Answer 14

cos(-u)=cos(u)
sec(-u)=sec(u)
y-axis is axis of symmetry

Question 15

odd functions

Answer 15

sin(-u)=-sin(u)
csc(-u)=-csc(u)
tan(-u)=-tan(u)
cot(-u)=-cot(u)

Question 16

Options for simplifying trig equations

Answer 16

1) Substitute with different expression
2) Factor
3) Get a common Denominator

Question 17

ways to solve single angles

Answer 17

1) collecting like terms
2) extracting square roots
3) factoring
4) applying “quadratic type”
5) rewriting with a single trig function
6) squaring and converting to quadratic type

Question 18

DeMoivre’s Theorem

Answer 18

z^n=r^n(cosnx+isinnx)

Question 19

Trig Form

Answer 19

z=r(cosx+isinx)

Question 20

Standard Form

Answer 20

a+bi

Question 21

Apparent vs Recurring

Answer 21

Apparent - each term is independent
Recurring- terms are related to each other

Question 22

Factorial

Answer 22

10!
10x9x8x7x6x5x4x3x2x1

Question 23

Summation Notation

Answer 23

n n=upper limit
∑ ai
i=1 i=lower limit

Question 24

arithmetic equations

Answer 24

∑ dn+c
n/2(a+an)
an=dn+c

Question 25

geometric equations

Answer 25

∑ a1(r)^n-1
Sn=a1(1-rn/1-r)
s=a^1/1-r ( |a| must be <1)

Question 26

(7x+2y)^15, n=8

Answer 26

15!/8!7! 6471 (7x)^8(2y)^7

Question 27

First Differences
2nd Common Ratio
Same Differences different signs
2nd Common Difference

Answer 27

First Differences - linear
2nd Common Ratio - exponential
Same Differences different signs - absolute value
2nd Common Difference - quadratic

Question 28

Mathematical Induction

Answer 28

1``````1)Prove P1 is true
2)Assume Pk is true
3)Prove Pk+1 is true