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Unit Circle Calculator
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Unit circle is a circle which is centered at origin and which has the radius of 1 unit. It is represented by the equation:
x2 + y2 = 1.
The values of x and y are given by trigonometric functions as x = sin $\theta$ and y = cos $\theta$
Hence the value of sin $\theta$ and cos $\theta$ should such that the sum of their squares should be equal to 1.

Unit Circle Calculator
calculates the sine, cosine and tangent values of any given angle which satisfies the equation:
x2 + y2 = 1.

 

Steps for Unit Circle Calculator

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Step 1 :  

Read the problem and observe the given angle.



Step 2 :  

Convert the given angle into radians. Find the Sine, cosine and tangent value of given angle and check whether it satisfies the relation:


x2 + y2 = 1. 



Problems on Unit Circle Calculator

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  1. The angle $\theta$ = 0 meets the unit circle at some values of sine and cosine and tangent. Calculates those values.


    Step 1 :  

    given: $\theta$ = 0o. To find the values of sine, cosine and tangent of the given angle and also to convert the given angle into radians.



    Step 2 :  

    The given angle can be converted to radians as below:


    0o  = $\frac{\pi}{180}$ $\times$ 0= 0 radians.


    x = sin $\theta$ = sin 0o = 0
    y = cos $\theta$ = cos 00 = 1
    tan $\theta$ = $\frac{sin \theta}{cos \theta}$


            = $\frac{0}{1}$


            = 0



    Answer  :  

    Hence 0o = 0 radians, (sin 0o, cos 0o) = (0,1) which satisfies the relation x2 + y2 = 1 and tan 0o = 0.



  2. Find the value of sine and cosine if angle $\theta$ meets the unit circle at 30o and also convert it to radians.


    Step 1 :  

    given: $\theta$ = 30o. To find the values of sine, cosine and tangent values of the given angle.



    Step 2 :  

    The given angle can be converted to radians as below:


    30o  = $\frac{\pi}{180}$ $\times$ 30= 0.523 radians.


    x = sin $\theta$ = sin 30o = 0.5
    y = cos $\theta$ = cos 30o = 0.867
    tan $\theta$ = $\frac{sin \theta}{cos \theta}$
    = $\frac{0.5}{0.867}$
    = 0.577.



    Answer  :  

    30o = 0.523 radians, (sin 30o, cos 30o) = (0.5, 0.867) which satisfies the relation x2 + y2 = 1 and tan 30o = 0.577.



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