Mathematics
ValorieLandstrom
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How to find exact value of tan 75°

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(2) Answers
bhani

If you have a scientific calculator, there will be a "tan" button. press that, then put the number "75" next to it. This will give you the exact answer. If you don't have a scientific calculator, then a tangent can easily be found by using a ratio: the side measurement opposite of 75º/the side measurement adjacent to 75º.

Polieke

[latex]tan \alpha = \frac{sin \alpha }{cos \alpha } \\--------\\\\tan75^0= \frac{\big{sin75^0}}{\big{cos75^0}} \\\\sin75^0=sin(45^0+30^0)=sin45^0\cdot cos30^0+sin30^0\cdot cos45^0=\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{ \sqrt{2} }{2} \cdot \frac{ \sqrt{3} }{2} + \frac{1}{2} \cdot\frac{ \sqrt{2} }{2} = \frac{ \sqrt{6}+ \sqrt{2} }{4} [/latex]

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