Posted by Jon on Thursday, February 14, 2008 at 3:28pm.
There are no typos and no work b/c I don't know how to do them. Thanks.
1)Find cos theta if sin theta=3/5 and 90 degrees<theta<180 degrees.
A)4/5
B)4/5
C)square root of 34/5
D)square root of 34/5
I chose A
2)Simplify:1csc^2theta/cot^2theta
A)1
B)1
C)tan^2theta
D)1/sin^4theta
I chose A
3)Simplify:5(cot^2thetacsc^2theta)
A)5
B)5
C)5csc^2 theta
D)5csc^2 theta
I chose B
4)Which expression is not equivalent to 1?
A)sin^2theta+cot^2thetasin^2theta
B)sin^2theta/1costheta 1
C)sec^2theta+tan^2theta
D)cot^2thetasin^2theta/cos^2theta
I chose C
5)Which expression is equivalent to tan thetasec theta/sin theta?
A)cot theta
B)cot theta
C)tan thetacot theta
D)tan thetasec^2theta
I don't know
6)Find the exact value of cos375 degrees.
A)square root of 6  square root of 2 over 4
B)square root of 6 + square root of 2 over 4
C)square root of 2  square root of 6 over 4
D) square root of 2  square root of 6 over 4
I chose B
Work for #1
1)Find cos theta if sin theta=3/5 and 90 degrees<theta<180 degrees.
A)4/5
B)4/5
C)square root of 34/5
D)square root of 34/5
I chose A
cos^2theta+sin^2theta=1
cos^2theta=1sin^2theta
cos^2theta=1(3/5)^2
cos^2theta=19/25
cos^2theta=16/25
=4/5
thats the only one that I can show work for.

math (#6 of 6)  drwls, Thursday, February 14, 2008 at 4:21pm
6. First of all, cos 375 = cos 15
Use the formula for cos (A  B), with A = 60 degrees and b = 45 degrees. If you don't know it, look it up.
You will need to use the facts that
cos 45 = sin 45 = (sqrt2)/2
cos 60 = 1/2
sin 60 = (sqrt 3)/2

#3 of 6  Guido, Thursday, February 14, 2008 at 4:57pm
We have this:
(3) Simplify:
5(cot^2thetacsc^2theta)
A)5
B)5
C)5csc^2 theta
D)5csc^2 theta
I chose A
You said B, right?
Let's see if that's true.
I will use x in place of theta to avoid having to write the word theta through and through.
So, x = theta.
cot^2 (x) = cos^2 (x)/sin^2 (x)
csc^2 (x) = 1/sin^2 (x)
We now have this:
5(cos^2 (x)/sin^2 (x)  1/sin^2(x) =
The trig terms within the parentheses become (sin^2(x)/sin^2(x)) = 1
We now have:
5 (1) = 5
I say the answer is choice A for question 3.
I hope this helps.
To solve the rest, use the equivalent trig identities. You can find the rest of the trig identities through an online search.
Done!

math  Jon, Thursday, February 14, 2008 at 5:14pm
#6)cos 375 = cos(60+45)
= cos 60 cos 45  sin 60 sin 45
= 1/2 x sqrt 2/2  sqrt 3/2 x sqrt 2/2
= sqrt 2 sqrt 6/4 which is C? If so, I understand how we got it. Thank you for helping me

math(#1 of 6)  Jon, Thursday, February 14, 2008 at 5:24pm
in my book its the same problem except its 3/5 and in my question its 3/5, so that would mean the final answer is 4/5 instead of 4/5 right?

math  Jon, Thursday, February 14, 2008 at 5:30pm
drwls, Thursday, February 14, 2008 at 5:24pm
Surely you meant to write cos 375 = cos 15
= cos (60  45)
No, I meant to write +

math  drwls, Thursday, February 14, 2008 at 6:32pm
60 + 45 is not 15

math  Jon, Thursday, February 14, 2008 at 5:33pm
thats how the formula is in my book but I see where you're coming from
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