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solve 83 with a right triangle and draw the triangle

Solve 83 With A Right Triangle And Draw The Triangle class=

Sagot :

We know that tan = opp / adj

arctan x = theta

Taking the tan of each side

x = tan theta = opp / adj

x/1 = tan theta

The hypotenuse :

We can find this using the pythagorean theorem

a^2 + b^2 = c^2

1^2 + x^2 = hyp ^2

The hypotenuse = sqrt( 1+x^2)

Now we can find the cos of the angle

cos theta = adj side/ hypotenuse

cos theta = 1/ sqrt(1+x^2)

Rationalizing the denominator

cos theta = sqrt(1+x^2)/ (1+x^2)

cos ( tan^-1 x) = sqrt(1+x^2)/ (1+x^2)

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