Math

QuestionFind the exact value of tan45\tan 45^{\circ}. What is tan45=\tan 45^{\circ}=? Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the exact value of tan45\tan45^{\circ}. . We are working in degrees, not radians.
3. We know that tanθ=sinθcosθ\tan \theta = \frac{\sin \theta}{\cos \theta}.

STEP 2

We know that sin45=cos45=12\sin45^{\circ} = \cos45^{\circ} = \frac{1}{\sqrt{2}} or 22\frac{\sqrt{2}}{2}.

STEP 3

Substitute these values into the formula for tanθ\tan \theta.
tan45=sin45cos45\tan45^{\circ} = \frac{\sin45^{\circ}}{\cos45^{\circ}}

STEP 4

Substitute the values of sin45\sin45^{\circ} and cos45\cos45^{\circ} into the equation.
tan45=2222\tan45^{\circ} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}

STEP 5

implify the fraction.
tan45=1\tan45^{\circ} =1So, the exact value of tan45\tan45^{\circ} is1.

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