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Find the value ofsin120.
A) 32
B) 32
C) 12
D) 12

Answer
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Hint: Draw a unit circle and chart out the trigonometric values on each quadrant of the circle. Find the value of sin120 or the value of sin120can be taken from the trigonometric table. Find either sine function or cosine function.

Complete step-by-step answer:
By using a unit circle we can find the value of sin120. Now let us draw a cartesian plane with x=cosθ and y=sinθ.
 Let us draw the trigonometric table as well:

sincostancotsecCosec
0010N.A1N.A
3012321332332
4512121122
6032123332233
9010N.A0N.A1


Now let us mark their values in the unit circle.
 
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Here, x=cosθ,y=sinθ.
Eg: -(cos30,sin30)=(x,y)
(x,y)=(32,12).
In the first quadrant, the values of cosθ and sinθ are positive.
In the second quadrant, the value of cosθ is negative and sinθ is positive.
In the third quadrant, both are negative.
In the fourth quadrant, cosθ is positive and sinθ is negative.
By looking into the figure, you can find that sin60=sin120.
i.e. sin60=sin120=32
Or if we are directly taking value from the trigonometric table, we need to find the value of sin120 by using other angles of sin functions such as 60 and sin180.
We know that 18060=120.
We also know that the trigonometric identity:
sin(180θ)=sinθ.
Put, θ=120.
sin(180120)=sin120sin60=sin120=32
From the trigonometric table, find the value of sin60=32.
Value of sin120=32
Option (a) is the correct answer.
Note:
We can also find the value of sin120 by using cosine function.
Using the trigonometry formula,
sin(90+θ)=cosθ
Thus to find the values of sin120, put θ=30
as, 90+30=120
sin(90+30)=cos30sin120=cos30
From trigonometric table, value of cos30=32
sin120=32.