Question

find the value of the following :-

sin(300) cosec(1050) - tan(-120)

Answer 1

@neer2890 @Kainui @IMStuck @Koikkara

Answer 2

Try your best first to attempt it.

Answer 3

sin(300) = -1/2 ..... is it ok

Answer 4

you can use the same method used by earlier to find their values.

Answer 5

is it ok ?

Answer 6

sin(300)=sin(90*3+30)
(90*3+30) indicates 4th quadrant in which sin theta is negative. so ans is negative.
also, multiple of 90 is odd, so sin changes to cos
sin(300)=- cos 30

Answer 7

sin(300)=- cos 30 how
?

Answer 8

it must be cosec I think

Answer 9

(90*3+30) is in 4th quadrant , so now we have to chk for the trignometric fxn associated with it. which is sin theta.
and sin is -ve in 4th quadrant. so a -ve sign should be associated with the answer.
also, multiple of 90 is odd, so sin changes to cos.
so sin(300)=-cos30

Answer 10

got it ?

Answer 11

ya

Answer 12

also, cosec(1050)=cosec(90*11+60)
(90*11+60) is in 4th quadrant in which cosec is negative, so a -ve sign is associated with the answer.
and multiple of 90 is odd , so cosec changes to sec.
so cosec(1050)=-sec60=-2

Answer 13

tan (-120)=-tan(120)=-tan(90*1+30)
(90*1+30) is in 2nd quadrant in which tan is -ve so a -ve sign is associated with the answer.
also, multiple of 90 is odd , so tan changes to cot.
so -tan(120)=-(-cot30)=cot30= sqrt(3)

Answer 14

\[\sin 300 cosec 1050- \tan(-120)= -\frac{ \sqrt{3} }{ 2 }*(-2)-\sqrt{3}=\sqrt{3}-\sqrt{3}=0\]

Answer 15

How to judge if 90*678 is in which quadrant ? @neer2890

Answer 16

and also when its 90*1159

Answer 17

we know we have 4 quadrants,check for multiple of 4

Answer 18

how ?

Answer 19

ok.
for e.g., \[90*4+ \Theta\]
is in 1st quadrant.
for 90*678=(90*(169*4+2))

Answer 20

so 90*169*4 is 4th quadrant and add 90*2 .
so 90*678=2nd quadrant

Answer 21

-tan(120)= -tan(90*1+30 ) .............. after that ?

Answer 22

@neer2890

Answer 23

= - cot 30 = - sqrt 3

Answer 24

as cot 30 = sqrt 3

Answer 25

ok.(90*1+30) is 2nd quadrant in which tan is negative. so extra negative sign is compulsory with answer.
als0, multiple of 90 is odd, so tan changes to cot
-tan(90*1+30)=-(-cot30)=cot30

Answer 26

in -(-cot 30), 1st minus sign is of -tan(120) and 2nd minus is because tan is -ve in 2nd quadrant.

Answer 27

No finally I got it Bhaiya

Answer 28

Yu Hu Thank You

Answer 29

you're welcome...:)

Answer 30

@neer2890 are you in IIT ?

Answer 31

no.. but i studied from IIT professors.