A bunch of trigonometry questions

[Justin218]

http://home.earthlink.net/~justincredible218/trig.jpg
Not supposed to use a calc on the ones above the line I drew. I don't really care about the answers, more about how to do each problem so I can learn to do other ones. I'd appreciate if any of you could help with some of them. Thanks!

 

[Justin218]

bump

 

[Muzzan]

First one:

We know that:

sin(a) = 0,8 <=> sin^2(a) = 0,64

We also know that:

cos^2(x) + sin^2(x) = 1 <=> cos(x)^2 = 1 - sin^2(x)

In our case: cos^2(a) = 1 - 0,8^2 = 0,36

The double angle formula:

cos(2x) = cos^2(x) - sin^2(x)

With x = a, we get:

cos(2a) = 0,36 - 0,64 = -0,28

 

[Heisenberg]

32)
sec(2x) = 1 / cos(2x)

As cos(2x) goes to 0, there will be an asymptote. Cos is 0 at pi/2, 3*pi/2, etc. Therefore x must be pi/4. Answer C.

 

[Justin218]

thanks for the help. does anyone know how to do 48? been trying to figure that one out at the moment...

 

[dym]

Originally posted by: Justin218
http://home.earthlink.net/~justincredible218/trig.jpg
Not supposed to use a calc on the ones above the line I drew. I don't really care about the answers, more about how to do each problem so I can learn to do other ones. I'd appreciate if any of you could help with some of them. Thanks!

tanx=tan6 -> x=6+k(pi)
the domain of x is [pi/2,pi]
6-pi=6-3.14=2.86 (k=-1)

Dun know wat other question U're stuck at...
I dun know if I could be any of help, but PM me if needed...
:beer: