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How do you evaluate #tan 45#?

Answer 1

James Adkins

Take a right triangle with equal side of length 1 hence by pythagorean theorem the hypotenuse is #sqrt2#.

Now #tan45=sin45/cos45=(1/sqrt2)/(1/sqrt2)=1#

In the right triangle above the angles are 90,45,45 because the triangle is isosceles.

Also in the triangle below we have that

sinA=(opposite side)/(Hypotenuse)

cosA=(adjacent side)/(Hypotenuse)

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Answer 2

Emery Adkins

To evaluate ( \tan(45^\circ) ), you use the definition of tangent as the ratio of the sine of the angle to the cosine of the angle. For ( 45^\circ ), both the sine and cosine are equal to ( \frac{\sqrt{2}}{2} ). So,

[ \tan(45^\circ) = \frac{\sin(45^\circ)}{\cos(45^\circ)} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.