Question

How to find sin 300 without calculator

Answer 1

@ganeshie8

Answer 2

sin 300 = sin(360-60) =-sin60 = -sqrt(3)/2= -0.866(appx)

Answer 3

sin(360-theta) is - sintheta?

Answer 4

yup

Answer 5

sin(360+-theta) is +- sintheta

Answer 6

oh depending upon the quadrant theta lies in

Answer 7

u knw \(\sin(A\pm B)\) formula right ?

Answer 8

yes

Answer 9

It would be a nightmare suppose apply it to sin 5000

Answer 10

\(\sin(360\pm \theta) = \sin 360 \cos \theta \pm \cos 360 \sin \theta = 0 \pm \sin \theta \)

Answer 11

such questions like sin 4000 and find cos 3500 come in exam so this identities won't be useful

Answer 12

i mean that was just an example, i know it won't be a perfect value

Answer 13

you may reduce sin(10^10000) easily, use below :

\(\large \sin(x \pm 360n) = \sin(x) \)

Answer 14

for less than 360

Answer 15

and for other 5 ratios

Answer 16

yes you can make it less than 360, and after that you can use other identities to compute the numerical value if possible. since sin is a periodic function of period 360 degrees, adding/subtracting 360 degrees will not change its value

Answer 17

may be lets work an example and see how this works ?

Answer 18

okay!

Answer 19

find the value of


\(\large \sin(360000000030) = ?\)

Answer 20

that goes into 360 perfectly

Answer 21

nope, look carefully again..

Answer 22

\[\sin(360000000030) = \sin(36000000000 + 30) \\= \sin (360n + 30) = \sin(30) = \dfrac{1}{2}\]

Answer 23

sin (9^9^9^9^9)

Answer 24

oh i see

Answer 25

that looks like a very interesting problem

Answer 26

\[\large \sin \left(9^{9^{9^{9^9}}}\right) = \sin \left(9^{9^{9^{9^9}}} \mod 360\right) \]

Answer 27

we need to find the remainder when 9^9^9^9 is divided by 360

Answer 28

yes i am trying but without calc how i would do i mean i can but still

Answer 29

may be, il let you figure it out, the answer is : \(\sin(9)\)

Answer 30

ok for tan 225

Answer 31

whats the period of tan ?

Answer 32

pi

Answer 33

180 in degrees

Answer 34

so adding/subtracting 180 degrees doesn't change the value of tan

Answer 35

it takes u back to ur older value

Answer 36

so,

\(\tan (x \pm 180) = \tan (x)\)

Answer 37

use it and reduce

Answer 38

i got it
for sin and cos adding and subtracting values from 360 will give the same answer
and subtracting it from 180 would give " - " of the answer

Answer 39

kindof, but its not a good idea to cram our heads with too many formulas

Answer 40

i will come back after some time sry

Answer 41

i think remembering below is sufficient :

1) period :
\(\sin (x \pm 360) = \sin (x)\)
\(\cos (x \pm 360) = \cos (x)\)
\(\tan (x \pm 180) = \tan (x)\)

2) angle sum/difference formulas

Answer 42

http://www.wolframalpha.com/input/?i=sin%289%5E9%5E9%5E9%5E9%29

Answer 43

laughing out loud

Answer 44

lol

Answer 45

i dont get it at all say for sin(x ± 360) = sin (x) .....what do you mean. like if you have 22..you to take away 360 or add. Im confused

Answer 46

You're correct monika :) take away 360 or add 360, the sin value will stay same.

Answer 47

for example :
sin(30 + 360) = sin(30)
sin(30 - 360) = sin(30

Answer 48

How would you know which one to do..take away or add? or do you just put the sign.
i thought it came about a different answer...thank you!

Answer 49

hmm we won't do anything unless it is required

Answer 50

to find \(\large \sin(390)\) , you will need to subtract 360

Answer 51

to find \(\large \sin (-330)\) , you will need to add 360

Answer 52

depends on what we need to find...

Answer 53

so sin(390) would end up .. sin( 390 - 360) = sin(30)?

Answer 54

Yes !

Answer 55

you're free to subtract as many 360's as you wish - the value will not change.

Answer 56

Thank you so so much!

Answer 57

sin(90+theta) = cos theta
cos(90+theta)= - sin theta
cos(180+theta)= -cos theta
tan(180 + theta) = tan theta