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What is the sine, cosine and tangent of 270 degrees?

Answer
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Hint: Express 270 into (270+θ) . Then we should use the following two identities for sin and cosine respectively, sin(270+θ)=cosθ and cos(270+θ)=sinθ . To find the tangent, we must remember that tanθ=sinθcosθ . In case the value of tangent is undefined, verify using the graph of y=tanθ at θ=270 to check whether it is + or  .

Complete step by step solution:
For sine of 270 degrees:
We can write 270 as (270+0) . Or, in equation form
sin(270)=sin(270+0)...(i)
We know the trigonometric identity sin(270+θ)=cosθ.
If we put θ=0 and keep in mind the fact that cos0=1 , we get
sin(270+0)=cos0=1...(ii)
Now substituting the value of sin(270+0) in equation (i), we get
sin(270)=1
Hence, the sine of 270 degrees is -1.

For cosine of 270 degrees:
We can write 270 as (270+0) . Or, in equation form
cos(270)=cos(270+0)...(iii)
We know the trigonometric identity cos(270+θ)=sinθ.
If we put θ=0 and keep in mind the fact that sin0=0 , we get
cos(270+0)=sin0=0...(iv)
Now substituting the value of cos(270+0) in equation (iii), we get
cos(270)=0
Hence, the cosine of 270 degrees is 0.

For tangent of 270 degrees:
We are well aware of the identity that
tanθ=sinθcosθ
Thus, we can write
tan270=sin270cos270
We can write 270 as (270+0) . Or, in equation form
tan(270+0)=sin(270+0)cos(270+0)
We can now substitute the values of sin(270+0) and cos(270+0) from equation (ii) and equation (iv) respectively. Thus, we have,
tan(270+0)=10 , which is N.D. or undefined.
Now, to check whether the value is + or  , we should use the graph of y=tan(x) at x=270

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From this graph, we can clearly see that y=tan(x) approaches + at x=270 .
tan(270)=+
Hence, the tangent of 270 degrees is positive infinity.

Note: We can express 270 degrees into multiple forms, such as, (270+0),(180+90) or (36090) . All of these forms could be used separately to find the trigonometric values of 270 . We should remember not to assume (10) as - when we are trying to find the tangent of 270.

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