Gr.11 functions formulas

Question 1

Relationship between arc length (l), radius (r), and angle (x)

Answer 1

x=l/r

Question 2

conversion between radians and degrees

Answer 2

rad/deg=pi/180

Question 3

sin2x=?

Answer 3

2sinxcosx

Question 4

2sinxcosx=?

Answer 4

sin2x

Question 5

ALL THREE:
cos2x=?

Answer 5

1. cos^2x-sin^2x
2. 2cos^2x-1
3. 1-2sin^2x

Question 6

tan2x=?

Answer 6

2tanx/(1-tan^2x)

Question 7

tanx=?

Answer 7

sinx/cosx

Question 8

to get the other two pythagorean identities, what do we divide the og by? (2)

Answer 8

1. sin^2x
2. cos^2x

Question 9

cos(A-B)

Answer 9

cosAcosB+sinAsinB
(cos both of them, switch the sign to plus, sin both of them) for cos (A-B)

Question 10

cos(A+B)

Answer 10

cosAcosB-sinAsinB
(same as cos(A-B): cos both, switch sign, sin both)

Question 11

sin(A-B)

Answer 11

sinAcosB-cosAsinB
(same sign, just memorize the order and its the same for sin(A+B)

Question 12

sin(A+B)

Answer 12

sinAcosB+cosAsinB
(same sign, just memorize the order and its the same for sin(A+B)

Question 13

what transformations:
y=-2cos[1/2(x+2)]-3

Answer 13

• reflection in x-axis
• vertical stretch by a factor of 2
• horizontal stretch by a factor of 2
• horizontal translation 2 units left
• vertical translation 3 units down

Question 14

what transformations:
y=1/3(2)^[-3(x-4)]+1

Answer 14

• vertical compression by a factor of 1/3
• reflection in y-axis
• horizontal compression by a factor of 1/3
• translation 4 right
• translation 1 unit up

Question 15

period when you know K?

Answer 15

P=2pi/K (absolute value of K)

Question 16

binomial theorem

Answer 16

(a+b)^n=a^n+nC1a^n-1b^1+….+b^n

Question 17

tn of arithmetic series

Answer 17

tn=a+(n-1)d

Question 18

sum of arithmetic series

Answer 18

a=n/2 [2a+(n-1)d]

Question 19

sum of infinite geometric series

Answer 19

S=1/(1-r)

Question 20

sum of geometric series

Answer 20

Sn=a(1-r^n)/1-r

Question 21

tn of a geometric series

Answer 21

ar^(n-1)