I think that I have a little problem with fundamental trigonometric identities. I am trying to answer it, but my webassign says I am wrong 3 times. Are you famailiar with webassign site? So, can you guys simplify cos^3(x) +sin^2 (x)cos(x) and cos x/tan x + and sec x? I am pretty stuck!!!

# Trigonometry

**Dhalsimowns**#2

All I remember about trig is that there is this 360 wheel diagram with all the angles and values, and that if you can read that you do like 75% of all trigonometry. Trig isreally easy once you have all that fundamental stuff down. Now it’s been six years since I did any of that, but I think your missing something simple. Your issue looks algebraic no?

**tanabe**#3

is this all one problem?

for cos^3(x) + sin^2(x)cos(x)

you can factor out a cos:

cos(x) cos^2(x) + sin^2(x) cos (x)

and since sin^2 + cos^2 = 1

you get:

cos^2(x)

someone double check me and i’m not 100% on the last part.

**Sleazoid**#4

cos^3(x) = cos^2(x)cos(x)

cos^2(x) + sin^2(x) = 1

cos^3(x) + cos(x)sin^2(x)

cos(x)cos^2(x) + cos(x)sin^2(x)

cos(x)[cos^2(x) + sin^2(x)]

cos(x)[1]

cos(x)

Can’t make anything of the second one. Trig wasn’t my strong point.

**Eshmasesh**#5

tan(x) = sin(x)/cos(x)

cos(x)/tan(x) = cos^2(x)/sin(x) = [1 - sin^2(x)]/sin(x) = 1/sin(x) - sin(x)

sec(x) = 1/cos(x)

cos(x) = sin(x)/tan(x), so 1/cos(x) = tan(x)/sin(x)

put that all together:

cos(x)/tan(x) + sec(x) = 1/sin(x) - sin(x) + tan(x)/sin(x) = [1 + tan(x)]/sin(x) - sin(x)

I’m not sure if that can be simplified further.

**tanabe**#6

for cos(x)/tan(x) + sec (x)

we know that tan(x) = sin/cos

so:

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

putting everything together we get:

cos^2(x)/sin(x) + sec(x)

and we know that sec(x) = 1/cos(x)

so:

cos^2(x)/sin(x) + 1/cos(x)

we can cancel out one of the cos to get our final answer:

cos(x)/sin(x)

again, not 100% but this is what i came up with.

**KaoriManabe**#8

if this were a word problem the triangle way is more helpful but

cscx - sinx = as simplified as you can get i guess

**tanabe**#12

damn man… i thought we were friends :sad:

imma go cut myself and use the blood to redo the problem.

in all seriousness, i redid the shit and got the same thing you did

**HBRD**#13

We need an SRK math thread. I could’ve used some help with pushdown automata a few hours ago :bluu:

**HBRD**#16

I’m bad with them (only been in the class for a little over a month now, but DFAs were the first thing we covered), but what’s the problem?

**Night**#17

I used to be one of those students where by senior year in high school I had to take a math class at college because I got too far. I can’t believe that back then I had to do that stuff. These days I have to punch in 2+2 on a calculator just to make sure it’s still 4…

**Eshmasesh**#18

Say that string x is a prefix of string y if a string z exists where xz = y and that x is a proper prefix of y if in addition x =/= y. In each of the following parts we define an operation on a language A. Show that the class of regular languages is closed under that operation.

a. NOPREFIX(A)= {w E A l no proper prefix of w is a member of A}

Not sure if this is within your scope but I don’t get this shit and the book doesn’t explain anything well.

**Sleazoid**#19

Precisely why simplifying trigonometric functions is :lame:

“That doesn’t look simple enough, I must’ve completely missed something. Better do it again.”