How do you evaluate #tan 45#?
Take a right triangle with equal side of length 1 hence by pythagorean theorem the hypotenuse is
Now 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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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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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.
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.
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.
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.

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