Melody

I have another method for the second question.  I found the exact answer and used no trig.

As others have already shown, triangle BEC is isosceles so BE=BC=8

DE=8-2=6 units.

Let angle ECD= alpha

It follows that in triangle BCD

< BCD = theta-alpha

< CDB =180-theta

< DBC = alpha

Now consider triangle ABE

<ABE = theta-alpha

<BEA=180-theta

<EAB = alpha

so 

Triangle BCD is similar to triangle ABE       (3 equal angles)

Hence

\(\frac{AB}{BE}=\frac{BC}{DC}\\ \frac{AB}{8}=\frac{8}{DC}\\ AB=\frac{64}{DC}\\\)

Also triangle ABC and triangle CED are both isosceles triangles with base angles of theta degrees so they are also similar.

so

\(\frac{AB}{BC}=\frac{DC}{DE}\\ \frac{AB}{8}=\frac{DC}{6}\\ AB=\frac{4*DC}{3}\\~\\ so\\~\\ \frac{64}{DC}=\frac{4*DC}{3}\\ \frac{64*3}{4}=DC^2\\ DC=\frac{8*\sqrt3}{2}\\ DC=4\sqrt3\;\;units\\\)

\(AB=\frac{64}{DC}\\ AB=\frac{64}{4\sqrt3}\\ AB=\frac{16}{\sqrt3}\\ AB=\frac{16\sqrt3}{3}\;\;units\\~\\ AB \approx 9.2376\;\;units\)

Expand using  cos(a+b)

Then simplify

X=5pi/4,  7pi/4

An FM radio station has a frequency of 88.9 MHz (megahertz). What is the wavelength in meters?

So this is     88.9 *10^6  wavelengths per sec     

The speed of radio waves is about     3*10^8 m/sec

\(\frac{3*10^8\;m}{1 sec} \times \frac{1sec}{88.9*10^6\;wavelengths}\\ \mbox{The seconds cancel out leaving you with}\\ =\frac{3*10^8\;m}{88.9*10^6\;wavelengths}\\ =\frac{3*10^2\;m}{88.9\;wavelengths}\\ =\frac{300\;m}{88.9\;wavelengths}\\ \approx \frac{3.375\;m}{1\;wavelengths}\\ \mbox{Wavelength is about 3.375m} \)

5 root of m10n6

I am going to interpret this as 

\(\sqrt[5]{m^{10}}*n^6\\ =(m^{10})^{1/5}*n^6\\ =m^2*n^6\\ =m^2n^6\\~\\ or\\~\\ \sqrt[5]{m^{10}n^6}\\ ={m^{2}n^{6/5}}\\ ={m^{2}n^{1.2}}\\\)

The terminal side of θ lies on the given line in the specified quadrant. Find the values of the six trigonometric functions of θ by finding a point on the line

You can use my pic to work them out for yourself. :)

    4,6,8,10,    divide into two         15,19,22,25

                               then divide into 4

4,           6 ,8,      10,                            15,        19,22,      25

(6+8)/2=7                                                    (19+22)/2=20.5

interquartile range = 20.5 - 7 = 13.5

I should have added the words "difference of"

11

For every 1 horizontal unit there are 11 vertical units.

So where is your question?