Trigonometry help wanted

**seasnake** · Jun20-09, 11:30 PM

Okay, I must admit, my trigonometry is rather awful...

anyway, I would like to write out what 1 / 2^2 is equal to in terms of sine, cosine, tangent, and the like

is the following correct, or how do I write it correctly (or what would be the correct figures for 0.5^0.5):

0.5^0.5 = a 45-degree angle = cos (45) = sin (45) = a tangent of 1

**Mentallic** · Jun21-09, 01:16 AM

Originally Posted by seasnake

is the following correct, or how do I write it correctly (or what would be the correct figures for 0.5^0.5):

0.5^0.5 = a 45-degree angle = cos (45) = sin (45) = a tangent of 1

Yes this is correct. What you are looking for is a value $LaTeX Code: \\theta$ where
$LaTeX Code: sin(\\theta)=\\frac{1}{\\sqrt{2}}$
And yes, you correctly noted that the isosceles right-angled triangle has adjacent and opposite sides (to the angle $LaTeX Code: \\theta$ ) of value 1 and hypotenuse of value $LaTeX Code: \\sqrt{2}$ .

Originally Posted by seasnake

anyway, I would like to write out what 1 / 2^2 is equal to in terms of sine, cosine, tangent, and the like

Did you mean 1/2^(1/2)? If you actually meant 1/4 then you wont have a 'nice' simple value for $LaTeX Code: \\theta$ . Don't worry, this isn't uncommon.

The best answer you can give for $LaTeX Code: \\theta$ to
$LaTeX Code: sin(\\theta)=\\frac{1}{4}$

Is: $LaTeX Code: \\theta=arcsin(\\frac{1}{4})\\approx 14.48^o$

this answer is just an acute angle, and I'm sure you're aware that there are more (actually, infinite) values of $LaTeX Code: \\theta$ that satisfy this result?

**seasnake** · Jun21-09, 04:03 AM

thanks... but I did mean exactly what I wrote 0.5^0.5, which equates to a value around .71something or other

**Mentallic** · Jun21-09, 04:08 AM

Yeah I thought so. It just put me off when you wrote:

Originally Posted by seasnake

I would like to write out what 1 / 2^2 is equal to

and the value .71 something IS $LaTeX Code: \\frac{1}{\\sqrt{2}}$ and isn't 1/2^2