Question

Tutorial
@blackbutterfly

Answer 1

Quadrant Law

Answer 2

just continue

Answer 3

Here, i have denoted angle with x

Answer 4

For finding an angle >90°

Answer 5

\(\bullet\) Break the angle into two parts such that 1\(^{st}\) part is multiple of 90° and 2\(^{nd}\) part is an acute angle

Answer 6

Example lets break 210°

Answer 7

can u ?

Answer 8

210° = 270°-60°

Answer 9

Here, 270° is a multiple of 90° (3*90) and 60° is an acute angle

Answer 10

ok ?

Answer 11

Waiting for ur response !

Answer 12

ah okay

Answer 13

where did you get 60 deg. ?

Answer 14

u have to guess it

Answer 15

Next step
\(\bullet\) Check the quadrant and determine the (+ve)/(-ve) sign

Answer 16

ah okay

Answer 17

210° = 270°-60° will lie in 3rd quadrant

Answer 18

In 3rd quadrant only tan/cot is +ve rest are -ve

Answer 19

ahh

Answer 20

Next Step
\(\bullet\) For (90°\(\pm\)X), (270°\(\pm\)X) function changes.
\(\bullet\) For (180°\(\pm\)X), (360°\(\pm\)X) function remains unchanged.

Answer 21

Sin will become cos, tan will become cot & cosec will become sec and vice versa

Answer 22

Here, we have Cos (270°-60°), so function will change and cos will become sin and since it is in 3rd quadrant it will be -ve.
So Cos (270°-60°) = -sin 60°

Answer 23

Getting it ?

Answer 24

yeah

Answer 25

Now we can easily find the value, sin 60° = \(\huge \frac{\sqrt{3}}{2}\), so -sin 60° = -\(\huge \frac{\sqrt{3}}{2}\)

Answer 26

Hence, cos 210° = -sin 60° = -\(\huge \frac{\sqrt{3}}{2}\)

Answer 27

what quadrant ?

Answer 28

IIIrd quadrant

Answer 29

See the diagram i made, it's self illustrative

Answer 30

I,II,III & IV represents the quadrants

Answer 31

I have indicated the angle range for each quadrant

Answer 32

ah how about in radians for example sin 2pi/3

Answer 33

u can convert them into degrees first. \(\huge\frac{2\pi}{3}\) rad = \(\huge\frac{2\pi}{3}\)* \(\huge\frac{180}{\pi}\) = 120°

Answer 34

got it ?

Answer 35

ah okayyy

Answer 36

There are two more principles
\(\bigstar\) Sin(-X) = -sinx, Cos(-x)=Cosx, tan(-x)= -tanX
\(\bigstar\) Sin(n360°=X)=SinX, Cos(n360°=X)=cosX, tan(n360°=X)= tanX

Answer 37

That's it !
Now all u need is practice.

Answer 38

are u willing to do some examples with me ?

Answer 39

how about cos 570

Answer 40

make it minus 360 = 210 III

Answer 41

ohkay..lets do it !

Answer 42

Cos 570° = Cos ((2*360°) - 150°)

Answer 43

=Cos 150°

Answer 44

= Cos (180°-30°)

Answer 45

It's in IInd quadrant and function will not change because its 180

Answer 46

So, Cos (180°-30°) = -Cos 30° = -\(\huge\frac{\sqrt{3}}{2}\)

Answer 47

Getting it ?

Answer 48

It is IIIrd quad right?

Answer 49

Cos 150° is in IInd quad

Answer 50

I mean 570

Answer 51

yep

Answer 52

@blackbutterfly is it clear ?

Answer 53

yeah thanks for the info.

Answer 54

\(\color{red}{\huge\bigstar}\huge\text{You're Most Welcome! }\color{red}\bigstar\)
\(~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{green}{\huge\ddot\smile}\color{blue}{\huge\ddot\smile}\color{pink}{\huge\ddot\smile}\color{red}{\huge\ddot\smile}\color{yellow}{\huge\ddot\smile}\)

Answer 55

are you teacher?

Answer 56

nopes !
http://openstudy.com/users/abhisar

Answer 57

we hav a chemistry subject too. the topic that i didnt understand is dimensional analysis about conversion

Answer 58

It's easy !

Answer 59

u wanna learn that too ?

Answer 60

yeah :D

Answer 61

ohkay brb !

Answer 62

okay wait

Answer 63

Wow, 14 medals...

Answer 64

15 :P

Answer 65

16.