Question

Expand and simplify...the drawing is down below

Answer 1

\[\sum_{n=1}^{3} 1/ n^3\]

Answer 2

expand!

Answer 3

i forgot how to @nphuongsun93 :(

Answer 4

\[\frac{1}{1^3}+\frac{1}{2^3}+\frac{1}{3^3}\]

Answer 5

would 1.16 be the answer?

Answer 6

yep

Answer 7

thank you, i also have another question... without a calculator, how would I determine the exact value of tan 7pi/4, tan 2pi/3, cot 11pi/4, and sin^-1(sin 7 pi/6)? do you happen to know how to do this? @nphuongsun93

Answer 8

yea. you will need to memorize the answers to sin(pi/4) and cos(pi/4), sin(pi/3) and cos(pi/3) though

Answer 9

what would be the answers to sin(pi/4) and all of what you said?

Answer 10

sin(pi/4) = sin(45degree) = sqrt(2)/2
cos(pi/4) = cos(45degree) = sqrt(2)/2
sin(pi/3) = sin(60degree) = sqrt(3)/2
cos(pi/3) = cos(60degree) = 1/2
sin(pi/6) = sin(30degree) = 1/2
cos(pi/6) = cos(30degree) = sqrt(3)/2

for example tan (7pi/4)

7pi/4 is in the quadrant 4 so sin is negative and cos is positive
tan (7pi/4) = sin (7pi/4)/cos (7pi/4) = -sqrt(2)/2 / sqrt(2)/2 = -1

Answer 11

so how would I solve tan 2pi/3? or sin^-1 (sin 7pi/6)? I don't understand what I'm confused about. @nphuongsun93

Answer 12

so how would I solve tan 2pi/3? or sin^-1 (sin 7pi/6)? I don't understand what I'm confused about. @nphuongsun93

Answer 13

do you understand how i got those answers and how i know when sin and cos are postive or negative?

Answer 14

I know why they are negative, how did you get the answers? are they off the unit circle?

Answer 15

2pi/3 = 120 degree
so sin 2pi/3 = sqrt3/2 and cos 2pi/3 = -1/2
understand this part?

Answer 16

yes

Answer 17

yea then tan = sin/cos

do you want to try (sin 7pi/6)?

Answer 18

so i would do sqrt 1/2?

Answer 19

for me i would try to find its angle in degree first and that would be 210degree and visualize this image
because it's in quadrant 3, both sin and cos are negative

sin 7pi/6 would be - 1/2