Question

Find the exact value of the following expression (multiple choice)

Answer 1

http://tigger.uic.edu/~calkafka/spring2011math121practiceexam3.pdf - number 17

Answer 2

method or answers?

Answer 3

method. i'll figure out the answer from the method..that way, i learn the method and figure the answer

Answer 4

or calculator?

Answer 5

k

Answer 6

number 1. think of a number (angle) between 0 and pi whose cosine is \[\frac{\sqrt{3}}{2}\]

Answer 7

look at trig cheat sheet here
http://tutorial.math.lamar.edu/cheat_table.aspx if you do not remember

Answer 8

Drawing pictures is SUPER helpful. The trig sheet Satellite mentioned is also very nice. :)

Answer 9

oh i only nueed help on number 17. thanks though

Answer 10

aaahhhhhhhh

Answer 11

Still,l a pic would help.
Lemmie sketch out one... brb.

Answer 12

addition angle formula:
\[sin(a+b)=sin(a)cos(b)+cos(a)sin(b)\]

Answer 13

You won't even have to do that, I think, cuz you have to do the inverse sin & cos stuff inside the main sin argument.

Answer 14

thats what i thought..at math teacher

Answer 15

i just dont know how to go about solving it

Answer 16

typeset is goofy but i assume it means
\[sin(sin^{-1}(\frac{2}{3}) + cos^{-1}(\frac{1}{3}))\]

Answer 17

yuppers. thats what it means

Answer 18

put \[a=sin^{-1}(\frac{2}{3}), b=cos^{-1}(\frac{1}{3})\]

Answer 19

use formula above. you aready know
\[sin(sin^{-1}(\frac{2}{3}))=\frac{2}{3}\]

Answer 20

you need \[cos^{-1}(\frac{2}{3})=\frac{\sqrt{5}}{3}\] by pythagoras

Answer 21

oops typo

Answer 22

you need \[cos(sin^{-1}(\frac{2}{3}))=\frac{\sqrt{5}}{3}\]

Answer 23

by pythagoras.

Answer 24

Here is the first part.

Answer 25

ahh the pythagorean thm

Answer 26

what math teacher said. you only need to find
\[sin(cos^{-1}(\frac{1}{3}))=\frac{\sqrt{2}}{3}\]

Answer 27

now you have everything you need to plug in to the "addition angle" formula

Answer 28

but i think you must use the formula now. you have all 4 numbers that you need.
\[sin(a)=\frac{2}{3}\]
\[cos(a)=\frac{\sqrt{5}}{3}\]

Answer 29

\[sin(b)=\frac{\sqrt{2}}{3}\]
\[cos(b)=\frac{1}{3}\]

Answer 30

write out the formula, substitute the numbers, and be done.

Answer 31

right. gimme a sec.

Answer 32

whoooooooooooops

Answer 33

\[sin(b)=\frac{\sqrt{8}}{3}\]

Answer 34

fraid both math teacher and i made a mistake.

Answer 35

its okay. i'm still working on it. thanks

Answer 36

if you look at the picture math teachers sent unfortunately the second triangle is wrong. adjacent side is 1, hypotenuse is 3, opposite side should be \[{\sqrt{8}}=2\sqrt{2}\]

Answer 37

get
\[\frac{2}{3}\times \frac{\sqrt{5}}{3}+\frac{1}{3}\times \frac{2\sqrt{2}}{3}\]

Answer 38

is the answer for number 17 "A"? thats what i'm getting. http://tigger.uic.edu/~calkafka/spring2011math121practiceexam3.pdf

Answer 39

Oh my gosh, I can't believe I did that. :( here is the corrected version.

Answer 40

dont worry mathteacher. satellite clarified. i'm debating on whether its A or B for number 17 in the link i posted

Answer 41

A yes!

Answer 42

SWEET!
thanky you so much!

Answer 43

welcome