Aus Online Mathematik Brückenkurs 1

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An often-used technique to calculate <math>\cos v</math> and <math>\tan v</math>, given the sine value of an acute angle, is to draw the angle <math>v</math> in a right-angled triangle which has two sides arranged so that <math>\sin v = 5/7\,</math>. [[Image:4_3_5_1.gif|center]] Using the Pythagorean theorem, we can determine the length of the third side in the triangle. {| align="center" ||[[Image:4_3_5_2.gif]] ||<math>\begin{align}&x^2 + 5^2 = 7^2\\[5pt] &\text{which gives that}\\[5pt] &x = \sqrt{7^2-5^2} = \sqrt{24} = 2\sqrt{6}\end{align}</math> |} Then, using the definition of cosine and tangent, {{Abgesetzte Formel||<math>\begin{align} \cos v &= \frac{x}{7} = \frac{2\sqrt{6}}{7}\,,\\[5pt] \tan v &= \frac{5}{x} = \frac{5}{2\sqrt{6}}\,\textrm{.} \end{align}</math>}} Note: The right-angled triangle that we use is just a tool and has nothing to do with the triangle that is referred to in the question.

• 4.3.5 - Solution - A right triangle with angle v and sides 5 and 7
• 4.3.5 - Solution - A right triangle with angle v and sides x, 5 and 7
• Vorlage:Abgesetzte Formel

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