`cos u = -4/5, pi/2

Wednesday, September 26, 2012

$\displaystyle{\cos{{u}}}=-\frac{{4}}{{5}},\frac{\pi}{{2}}$

By the double angle formulas

$\displaystyle{\cos{{\left({2}{u}\right)}}}={2}{{\cos}}^{{2}}{u}-{1},$

$\displaystyle{\sin{{\left({2}{u}\right)}}}={2}{\sin{{\left({u}\right)}}}{\cos{{\left({u}\right)}}}.$

By the first formula $\displaystyle{\cos{{\left({2}{u}\right)}}}={2}\cdot{{\left(-\frac{{4}}{{5}}\right)}}^{{2}}-{1}=\frac{{7}}{{25}}.$

Because $\displaystyle{u}$ is in the second quadrant, its sinus is positive and is equal to

$\displaystyle\sqrt{{{1}-{{\cos}}^{{2}}{u}}}=\frac{{3}}{{5}}.$

So by the second formula $\displaystyle{\sin{{\left({2}{u}\right)}}}={2}\cdot\frac{{3}}{{5}}\cdot{\left(-\frac{{4}}{{5}}\right)}=-\frac{{24}}{{25}}.$

And $\displaystyle{\tan{{\left({u}\right)}}}=\frac{{\sin{{\left({u}\right)}}}}{{\cos{{\left({u}\right)}}}}=-\frac{{24}}{{7}}.$

The answer: $\displaystyle{\sin{{\left({2}{u}\right)}}}=-\frac{{24}}{{25}},$ $\displaystyle{\cos{{\left({2}{u}\right)}}}=\frac{{7}}{{25}},$ $\displaystyle{\tan{{\left({2}{u}\right)}}}=-\frac{{24}}{{7}}.$

Blog

Wednesday, September 26, 2012

$\displaystyle{\cos{{u}}}=-\frac{{4}}{{5}},\frac{\pi}{{2}}$

No comments:

Post a Comment

What was the device called which Faber had given Montag in order to communicate with him?