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:1-csc^2theta/cot^2theta
A)-1
B)1
C)tan^2theta
D)1/sin^4theta
I chose A
3)Simplify:-5(cot^2theta-csc^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/1-costheta -1
C)sec^2theta+tan^2theta
D)cot^2thetasin^2theta/cos^2theta
I chose C
5)Which expression is equivalent to tan theta-sec theta/sin theta?
A)-cot theta
B)cot theta
C)tan theta-cot theta
D)tan theta-sec^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=1-sin^2theta
cos^2theta=1-(3/5)^2
cos^2theta=1-9/25
cos^2theta=16/25
=4/5
thats the only one that I can show work for.
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
We have this:
(3) Simplify:
-5(cot^2theta-csc^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!
#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
Surely you meant to write cos 375 = cos 15
= cos (60 - 45)
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?
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 +