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How do you find the value of cos120?

Answer
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Hint: The given question is to find out the value of the given trigonometric ratio. Since there are a total six trigonometric ratios in trigonometry. Which are sinθ, cosθ, tanθ, cosecθ, secθ, cotθ with an angleθ. Also these six trigonometric ratios have specific or fixed values at some fixed angles, which are 00, 300, 450, 600 and 900 . Value of Trigonometric ratios at these angles is fixed. Also these angles are in degrees and we are also have angles whose values for 300, 450, 600 and 900 are π6, π4, π3and π2 respectively where π=1800(in radians)

Complete Step by step Solution:
The given question is to find out the value of the given trigonometric ratio. Since-there are six trigonometric ratios whose value of r some specific angle is fixed
Since angle is in degree as well as in radians.
and the fixed values of the trigonometric ratios at certain angles which are 300, 450, 600 and 900 were angle in degree
Also angles in radians in radians is symbolized in terms of 300, 450, 600 and 900π where value of in radians is 1800
Therefore angles in degrees and radians are
00, 300, 450, 600 and 900 is equivalent to 0,π6, π4, π3, π2 where π=1800are given as
And the fixed values for sinθ and cosθ are given as

angles00 300 450600900
sinθ04=014=1214=12=1234=2244=1
cosθ13212120


Value of sinθ are derived as talking 0 , 1 , 2 , 3 ,4
Dividing all by 4 and taking square roots and the values obtained are the values of sinθ at angle 00, 300, 600, 450900
and value of cosθ are derived by taking the inverse of all the values of sinθ for angles 00, 300, 600, 450 and 900
Means sin00=cos900, sin300=cos600, sin450=cos450, 
sin600=cos300 and sin900=cos00

 Since we want to find out the value of cos1200 But the value of 1200 angle is not known to us.
Also we can write 1200as (900+300)
Therefore cos1200 becomes cos(900+300)
Which becomes – sin300
By using identity cos(900+300)=sinθ
So value of sin300 is 12
Therefore sin300=12
So, value of cos1200 is 12

Note: The angles in degree as well as in radians are having fixed value for the fixed trigonometric ratio where angle in degree is denoted by degree after the angle and in radians is denoted by using.
π where π=1800 which is the relation to convert degree to radiation in trigonometry

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