How do you find exact value of \tan(\pi/4)?



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How do you find exact value of tan(π4)?

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Macsen Nixon

Macsen Nixon

Skilled2021-10-26Added 117 answers

Given: tan(π4)
The cousine is defined as the opposite leg divided by the hypotenuse of a rectangular triangle, while the sine is defined as the adjacent leg divided by the hypotenuse.
sin(π4)=adjacent leghypotenuse
cos(π4)=opposite leghypotenuse
By the Pythagorean theorem a2+b2=c2 where a (adjacent) and b (opposite) are the legs and c is the hypotenuse c. This then implies that c=a2+b2 for the hypotenuse c.
However, if one of the angles of the triangle is 45 or π4, then the triangle is isosceles and thus the two legs have the same length a=b
The tangent is the sine divided by the cousine:
Result: 1

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