Expert: Paul Klarreich - 1/21/2008

Question
QUESTION: Can you please help me with these problems! they are based on trig idenities.

Use sum formula..
1. sin(x+pi/3)=___sin(x)+___cos(X)

sum or difference formula..
2. sin(pi/12)=
3. sin(pi/8)=
4. cos(pi/12)=
5. cos(pi/8)=

Simplify and write trig expression in terms of sine and cosine.
6. (1-cosy)(1+cosy)=(f(y))^2
   f(y)=______


Answers in fraction..
if Tan(angle)= -3/4 and cos(angle)>0 then
sin=
cos=
tan=

use sum formula to fill in the blanks in the identity below.
can't use decimals on this one..
sin(x+pi/3)=____sin(x)+____cos(x)


Ok.. well I'm having trouble with my webwork,it's online so it tells me if my answer is right or wrong. well heres what I got for some of my answers but they are wrong, and I have no idea what I did wrong..(I put MY answers in blanks)

1. A,B,C,D,E are identities, and 1,2,3,4,5 are expressions. I'm supposed to match them. (I have put my answers on the blanks)

A. Tan(x)
B. Cos(x)
C. Sec(x)csc(x)
D. 1-(cos(x))^2/cos(x)
E. 2sec(x)

_B_ 1. Sin(x)Tan(x)
_A_ 2. sin(x)sec(x)
_C_ 3. tan(x)+cot(x)
_D_ 4. sec(x)-sec(x)(sin(x))^2
_E_ 5. cos(x)/1-sin(x)+ 1-sin(x)/cos(x)

2.for each trig expression A,B,C,D,E, choose the expression from 1,2,3,4,5 that completes a fundamental identity.
A.(sin)^2+(cos)^2
B.sinx/cosx
C.(tanx)^2+1
D.cosx/sin(x)
E.(sinx(^2

_e_1. 1-(cosx)^2
_b_2. tanx
_a_3. 1
_d_4. cotx
_c_5. (secx)^2

Each expression simplifies to a contant, a single trig function or a power of a trig function. Use fundamental ideneties to simplify each expression.

1. sin(x)tan(x)/cos(x)=__tan^2x
2. sec(x)cos(x)=__1__
3. (tan(x))^2+sin(x)csc(x)=__tanx^2+1___
4. (sec(x))^2-1=__tan^2__
5. tan(x)cos(x)=__sin__

Simplify and write the trif expression in terms of sin and cosine:
tanxcscx=1/f(x)
f(x)=_cos___
^^i don't know how to do that one neither! but i tried and thats what I got..



ANSWER: Questioner:   dana
Category:  Advanced Math
Private:  No
 
Subject:  trig
Question:  Can you please help me with these problems! they are based on trig identities.
............................................
Hi, Dana,

This is a lot of questions, but most seem short, and I will just get you started on most.

You will use these basic 'special angle' values:

sin(pi/6) = 1/2
cos(pi/6) = sqrt(3)/2
sin(pi/3) = sqrt(3)/2
cos(pi/3) = 1/2
sin(pi/4) = sqrt(2)/2
cos(pi/4) = sqrt(2)/2



Use sum formula..
1. sin(x+pi/3)=___sin(x)+___cos(X)

sin(x+pi/3) = sin x cos pi/3 + sin pi/3 cos x


sum or difference formula..
2. sin(pi/12)= sin(pi/3 - pi/4) = ....
3. sin(pi/8)= sin((pi/4)/2) = use half-angle formula.
4. cos(pi/12)= see #2
5. cos(pi/8)= see #5

Simplify and write trig expression in terms of sine and cosine.
6. (1-cosy)(1+cosy)=(f(y))^2

= 1 - cos^2(y) = sin^2(y)

  f(y)=______


Answers in fraction..
if Tan(angle)= -3/4 and cos(angle)>0 then

If cos (t) > 0 and tan < 0, this is Quad II.
Set  x = -3, y = 4, find r = 5, etc.


sin=
cos=
tan=

use sum formula to fill in the blanks in the identity below.
can't use decimals on this one..
sin(x+pi/3)=____sin(x)+____cos(x)

See #1, above.


Ok.. well I'm having trouble with my webwork,

>> What's web work?

it's online so it tells me if my answer is right or wrong. well heres what I got for some of my answers but they are wrong, and I have no idea what I did wrong..(I put MY answers in blanks)

1. A,B,C,D,E are identities, and 1,2,3,4,5 are expressions. I'm supposed to match them. (I have put my answers on the blanks)

A. Tan(x)
B. Cos(x)
C. Sec(x)csc(x)
D. 1-(cos(x))^2/cos(x)
E. 2sec(x)

_B_ 1. Sin(x)Tan(x)  D
_A_ 2. sin(x)sec(x)  OK.
_C_ 3. tan(x)+cot(x) OK
_D_ 4. sec(x)-sec(x)(sin(x))^2  B
_E_ 5. cos(x)/1-sin(x)+ 1-sin(x)/cos(x)    OK

2.for each trig expression A,B,C,D,E, choose the expression from 1,2,3,4,5 that completes a fundamental identity.
A.(sin)^2+(cos)^2
B.sinx/cosx
C.(tanx)^2+1
D.cosx/sin(x)
E.(sinx(^2

_e_1. 1-(cosx)^2  OK
_b_2. tanx   OK
_a_3. 1  Ok
_d_4. cotx  OK
_c_5. (secx)^2  OK

Each expression simplifies to a contant, a single trig function or a power of a trig function. Use fundamental ideneties to simplify each expression.

1. sin(x)tan(x)/cos(x)=__tan^2x    OK
2. sec(x)cos(x)=__1__       OK
3. (tan(x))^2+sin(x)csc(x)=__tanx^2+1___  = sec^2(x)
4. (sec(x))^2-1=__tan^2__       OK
5. tan(x)cos(x)=__sin__   OK

Simplify and write the trif expression in terms of sin and cosine:

tanxcscx=1/f(x) = cos x, so  f(x) = 1/cos x
f(x)=_cos___


---------- FOLLOW-UP ----------

QUESTION: I'm sorry I'm still very confused on the following problems please help if you can.Well I think they are all the same concept, so if you can explain me one i would very much appreciate it.

Simplify and write the trig expression in terms of sine and cosine.

1. sin(x)+cot(x)cos(x)=1/f(x)
f(x)=____
2. cos(x)sec(x)/tan(x)=f(x)/g(u)
f(x)=
g(x)=
3.tan(x)+cot(x)=1/f(x)
f(X)=  

Answer
Questioner:  dana
Private: no


QUESTION: I'm sorry I'm still very confused on the following problems please help if you can.Well I think they are all the same concept, so if you can explain me one i would very much appreciate it.

Simplify and write the trig expression in terms of sine and cosine.

1. sin(x)+cot(x)cos(x)=1/f(x)
f(x)=____

sin(x)+cot(x)cos(x) =
       cos x
sin x + ------ cos x =
       sin x

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

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

 1         1
------- = ----
sin x    f(x)

Looks like f(x) = sin x

..................................
2. cos(x)sec(x)/tan(x)=f(x)/g(x)  << did you mean g(u)?
f(x)=
g(x)=

cos(x)sec(x)/tan(x) =
   
1/tan x, because cos x sec x = 1
 cos x
= ------
 sin x

3.tan(x)+cot(x)=1/f(x)
f(X)=

tan(x)+cot(x) =
sin x    cos x
------ + ------ =
cos x    sin x
sin^2(x) + cos^2(x)
------------------- =
cos x sin x

    1          1
------------- = ----, etc.
cos x sin x    f(x)