Question #50c05

Question

Question #50c05

1 Answer

Impact of this question

1164 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-11T05:55:38

0.18;
- 5.64

Explanation:

Find $tan (\frac{x}{2})$ $tan (x/2)$ by calculator.

tan x = 0.366 --> Calculator gives --> 2 solutions -->
a. $x = 20^{\circ} 10$ $x = 20^@10$ --> $\frac{x}{2} = 10^{\circ} 05$ $x/2 = 10^@05$ --> $tan (\frac{x}{2}) = 0.177$ $tan (x/2) = 0.177$
b. $x = 20.10 + 180 = 200^{\circ} 10$ $x = 20.10 + 180 = 200^@10$ --> $\frac{x}{2} = 100^{\circ} 05$ $x/2 = 100^@05$
$tan (\frac{x}{2}) = tan (100.05) = - 5.64$ $tan (x/2) = tan (100.05) = - 5.64$
Note. You can also evaluate $tan (\frac{x}{2})$ $tan (x/2)$ by using trig formula:
$tan x = \frac{2 tan (\frac{x}{2})}{1 - {tan}^{2} (\frac{x}{2})} = 0.366$ $tan x = (2tan (x/2))/(1 - tan^2 (x/2)) = 0.366$
Solve this quadratic equation for $tan (\frac{x}{2}) = t$ $tan (x/2) = t$
$0.37 t^{2} + 2 t - 0, 37 = 0$ $0.37t^2 + 2t - 0,37 = 0$
$D = d^{2} = b^{2} - 4 a c = 4 + 0.55 = 4.55$ $D = d^2 = b^2 - 4ac = 4 + 0.55 = 4.55$ --> $d = \pm 2.13$ $d = +- 2.13$
There are 2 real roots:
$tan (\frac{x}{2}) = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{2}{0.74} \pm \frac{2.13}{.74} = - 2.70 \pm 2.88$ $tan (x/2) = -b/(2a) +- d/(2a) = -2/0.74 +- 2.13/.74 = - 2.70 +- 2.88$
$tan (\frac{x}{2}) = t = - 2.70 - 2.88 = - 5.58$ $tan (x/2) = t = - 2.70 - 2.88 = - 5.58$ OK
$tan (\frac{x}{2}) = t = - 2.70 + 2.88 = 0.18$ $tan (x/2) = t = - 2.70 + 2.88 = 0.18$ OK

Science

Math

Humanities

... and beyond

Question #50c05

1 Answer

Explanation:

Related questions

Impact of this question