
What is the sine, cosine and tangent of 270 degrees?
Answer
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Hint: Express . Then we should use the following two identities for sin and cosine respectively, . To find the tangent, we must remember that . In case the value of tangent is undefined, verify using the graph of to check whether it is .
Complete step by step solution:
For sine of 270 degrees:
We can write . Or, in equation form
We know the trigonometric identity .
If we put and keep in mind the fact that , we get
Now substituting the value of in equation (i), we get
Hence, the sine of 270 degrees is -1.
For cosine of 270 degrees:
We can write . Or, in equation form
We know the trigonometric identity .
If we put and keep in mind the fact that , we get
Now substituting the value of in equation (iii), we get
Hence, the cosine of 270 degrees is 0.
For tangent of 270 degrees:
We are well aware of the identity that
Thus, we can write
We can write . Or, in equation form
We can now substitute the values of from equation (ii) and equation (iv) respectively. Thus, we have,
, which is N.D. or undefined.
Now, to check whether the value is , we should use the graph of
From this graph, we can clearly see that .
Hence, the tangent of 270 degrees is positive infinity.
Note: We can express 270 degrees into multiple forms, such as, . All of these forms could be used separately to find the trigonometric values of . We should remember not to assume when we are trying to find the tangent of .
Complete step by step solution:
For sine of 270 degrees:
We can write
We know the trigonometric identity
If we put
Now substituting the value of
Hence, the sine of 270 degrees is -1.
For cosine of 270 degrees:
We can write
We know the trigonometric identity
If we put
Now substituting the value of
Hence, the cosine of 270 degrees is 0.
For tangent of 270 degrees:
We are well aware of the identity that
Thus, we can write
We can write
We can now substitute the values of
Now, to check whether the value is

From this graph, we can clearly see that
Hence, the tangent of 270 degrees is positive infinity.
Note: We can express 270 degrees into multiple forms, such as,
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