Melody

You can draw a right angled isosceles triangle.

Let the equal sides by 1 unit

The equal angles will be 45 degrees

Using Pythagoras' theorum you can determing that the hypotenuse is sqrt(2)

Then you can reas cos 45degrees straight off the triangle

$$cos 45 = \frac{1}{\sqrt2}\\$$

if you want to have a rational denominator then

$$cos 45 = \frac{1}{\sqrt2}=\frac{1}{\sqrt2}\times \frac{\sqrt2}{\sqrt2}=\frac{\sqrt2}{2}\\$$

Inverse sine is the same as arc sine  so just use asin   

Do you mean  

$$\\64 cm^2 = \sqrt{x^2+16} cm^2\\
or\\
64 cm^2 = \sqrt{x^2}+16 cm^2\\
or\\
something\;\;else?$$

^ the proper name for this caret

(don't confuse it with a 'carrot' that a rabbit might eat or a 'carat' which is a unit of weight for gemstones)

However when used as a 'power of', exponent symbol it is called a 'hat'

4^3 means 4³ which means 4 x 4 x 4 = 64

 You have to have something after the ^ or id doesn't make sense.  

The web2calc on the home page has log and 10^x displayed all the time at the bottom of the calculator.

If you put your curser over either of these then ln, e^x appears below and log₂,  2^x  appears below that.

So log base 10 is log and antilog base 10 is  10^x

Log base e is ln and antilog base e is e^x

Log base 2 is log₂ and antilog base 2 is 2^x

You can also type these straight into the input area at the top of the calculator.

I am sure that if I have said anything incorrect someone will correct me.  

$$\\tan(sin^{-1}\left(\frac{-\sqrt3}{2}\right))\\\\
\mbox{Consider }\qquad sin^{-1}\left(\frac{-\sqrt3}{2}\right)\\\\
\frac{-\pi}{2}\le sin^{-1}\left(\frac{-\sqrt3}{2}\right)\le \frac{\pi}{2}\\\\
\mbox{The inverse sine is negative so the angle is in the 4th quad}\\
\mbox{Keep this in mind but look for the equivalent 1st quadrant answer}\\$$

$$\\sin^{-1}\left(\frac{\sqrt3}{2}\right)=60^0\\\\
tan60^0=\sqrt3\\$$

But it is  not really 60degrees    $$\frac{\pi}{3}\;radians$$    because it is in the 4th quad i.e.  $$\frac{5\pi}{3}$$  radians

So therefore the answer is $$-\sqrt{3}$$

$$\\tan(sin^{-1}\left(\frac{-\sqrt3}{2}\right))=\;-\sqrt3$$

12% pa,

2months is 2/12 = 1/6 of a years so interest it 12/6=2%

2% of 1000 pounds = 0.02*1000 = 20 pounds

WOW IT does too.   

NO NEITHER DO i!!