Question

Calculus,

Can you please help me solve this exersise ? http://screencast.com/t/ZCxLNCfm

Thanks a lot

Answer 1

you have a unit circle with u ?

Answer 2

Unfortunately I am not sure what that is :/

Answer 3

http://en.wikipedia.org/wiki/File:Unit_circle_angles_color.svg

Answer 4

ok

Answer 5

in that chart,
the point is of the form (r cos theta, r sin theta)
with r=1 (because of "unit")

Answer 6

hey @hartnn dont you think you shud better suggest a trig table?

Answer 7

so, where do u see the point where sin theta = -1 ??
(for sin^{-1} -1)

Answer 8

table or circle, both give same info

Answer 9

pi/2 ?

Answer 10

for pi/2, the y co-ordinate (sin ) is +1 right ?

Answer 11

where is y co-ordinate = -1 ?
for which angle ?

Answer 12

oh is it - pi/2 ?

Answer 13

what do you mean which angle

Answer 14

yes, -pi/2 or 3pi/2
is the correct angle

Answer 15

all those are angels
0,pi/2,3pi/2,2pi

Answer 16

so sin is -1 in those angles ?

Answer 17

sin is -1 for -pi/2. 3pi/2 , 3pi/2 +2pi, and so on

Answer 18

so the answer ot the first is -pi/2 ?

Answer 19

Or I can also put 3pi/2 ?

Answer 20

both are valid

Answer 21

so can u also find c and d now ?

Answer 22

Ok but why does it have a power of -1 above the sin ? How am I using the ^-1 information ?

Answer 23

ok, its the inverse sin function!
when
\(\sin x =y \implies x = \sin^{-1}y\)
also called arcsin y

Answer 24

So sin (-1) (without the power) = -2/pi too ? or no ?

Answer 25

I mean without the "inverse" sing **

Answer 26

sin (-1) what that is ?
sin of the angle -1 ?

Answer 27

theta = -1

Answer 28

sin (-1) = -sin 1 ....is just a small number .....not in terms of pi

Answer 29

cant sin^(-1)(-1) be = -sin^(-1)(1) ? :P you see what I mean ?

Answer 30

yes, thats true too, because sin -x = -sin x

Answer 31

so, sin^-1 -1 = - sin^-1 1 = - (pi/2)
which i said is valid too :)

Answer 32

so why if we put the inverse sign that grants us the bility to express it in terms of pi and without the inverse sign we can't do that?

Answer 33

hmm

Answer 34

because \(\sin^{-1}.....\) will give you AN ANGEL!

Answer 35

oooh

Answer 36

because we always take sin of angels!

Answer 37

second one is pi/2 or 0 ?

Answer 38

and/or ****

Answer 39

forget about tan inverse for now,
first do c and d
by looking at unit circle

Answer 40

ok hold on

Answer 41

c is pi/3 ?

Answer 42

pi/6 * * * *

Answer 43

pi/3 right ?
because sin inverse
and you see y co-ordinate for sin

Answer 44

I see. Is 2pi/3 correct as well ?

Answer 45

yes, yes, good

Answer 46

what about d ?
which 2 angles ?

Answer 47

pi/3 and 5pi/3

Answer 48

wasn't that easy ? :)
now sec^{-1}-2 = cos^{-1} (-1/2) = ... ?

Answer 49

hmmm 2pi/3 and 4pi/3 ? Btw how did you make that conversion inside the parenthesis ? (-2) = (-1/2)

Answer 50

have a look at inverse trogo formulas whn u have time
http://en.wikipedia.org/wiki/Inverse_trigonometric_functions

Answer 51

there's a formula for that

Answer 52

hmm i see

Answer 53

the 1st one in reciprocal arguments

Answer 54

so only tan inverse remains, right ?

Answer 55

yea !

Answer 56

you know tan = sin/cos
so, tan =1 only when sin = cos
right ??
so for what values of angles, are sin and cos equal ?? find that from circle

Answer 57

pi/4 , 5pi/4 ??

Answer 58

:) correct!

Answer 59

because for tan pi/4 and tan 5pi/4, the answer will be =1

Answer 60

hence tan inverse of 1 will be pi/4 or 5pi/4

Answer 61

:D I see ! ! Thanks a lot for the clarifications ! ^_^

Answer 62

welcome ^_^