Trigonometry Help: Understanding 1/2^2 in Terms of Sine, Cosine, and Tangent

[seasnake]

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]

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 [itex]\theta[/itex] where
[tex]sin(\theta)=\frac{1}{\sqrt{2}}[/tex]
And yes, you correctly noted that the isosceles right-angled triangle has adjacent and opposite sides (to the angle [itex]\theta[/itex]) of value 1 and hypotenuse of value [itex]\sqrt{2}[/itex].

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 won't have a 'nice' simple value for [itex]\theta[/itex]. Don't worry, this isn't uncommon.

The best answer you can give for [itex]\theta[/itex] to
[tex]sin(\theta)=\frac{1}{4}[/tex]

Is: [tex]\theta=arcsin(\frac{1}{4})\approx 14.48^o[/tex]

this answer is just an acute angle, and I'm sure you're aware that there are more (actually, infinite) values of [itex]\theta[/itex] that satisfy this result?

 

[seasnake]

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

 

[Mentallic]

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

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

and the value .71 something IS [tex]\frac{1}{\sqrt{2}}[/tex] and isn't 1/2^2