Math Help Forum - View Single Post - Well these are a teaser too..Trigonometry

running-gag · #2 December 4th, 2008, 09:48 AM

Look at the trigonometric circle

$sin(2\theta) = -\frac{1}{2}$

gives $2\theta = -30 + 360k$ or $2\theta = -150 + 360k$ with k integer

Therefore $\theta = -15 + 180k$ or $\theta = -75 + 180k$

Solving the equation for solutions in the interval [0, 360[

$S = {105, 165, 285, 345}$

$\frac{\sqrt{3}}{cos(2\theta)} = 2$

$cos(2\theta) = \frac{\sqrt{3}}{2}$

$2\theta = -30 + 360k$ or $2\theta = 30 + 360k$

$\theta = -15 + 180k$ or $\theta = 15 + 180k$

Solving the equation for solutions in the interval [0, 360[

$S = {15, 165, 195, 345}$