Question

7.
Which of the following is positive number?
(1) sin 1290
(3) cot 1200
(2) cos570
(4) tan960​

Answer 1

Answer:

answer in Short cut ( 4)

Step-by-step explanation:

tan 960= tan(2(2π) + π) +π/6

= tan (π+ π\3)

= tan π\3

=√3

Answer 2

In given options (4) tan 960​ will have positive value

Given:

(1) sin 1290     (2) cos 570

(3) cot 1200    (4) tan 960 ​

To find:

Which of the above will be a positive number ?

Solution:

Formulas used

sin (n∙360°+θ) = sin θ                sin (180° + θ) = - sin θ

cot (n∙360°+θ) = cot θ               cos (180° + θ) = - cos θ  

cos (n∙360°+θ) = cos θ              cot ( 90° + θ) = - tan θ

tan (n∙360°+θ) = tan θ               tan (180° + θ) = tan θ

(1) sin 1290

⇒ Sin (3*360 + 210)          [ ∵ 1290 = 3×360 + 210 ]

⇒ Sin 210

⇒ Sin (180+ 30)  

⇒ -Sin 30 = -1/2

(2) Cos 570  

⇒ Cos (360 + 210)

⇒ Cos 210

⇒ Cos (180+ 30)

⇒ - Cos 30 = - √3/2

(3) Cot 1200

⇒  Cot (3*360 + 120)

⇒  cot 120

⇒  cot (90+30)

⇒  - tan 30 = - 1/√3

(4) tan 960​

⇒  tan (2*360 +240)

⇒  tan 240

⇒  tan (180 + 60)

⇒  tan 60 = √3

Therefore, In given options (4) tan 960​ will have positive value

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