Wednesday

October 7, 2015
Posted by **Jon** on Thursday, February 14, 2008 at 3:28pm.

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.

- math (#6 of 6) -
**drwls**, Thursday, February 14, 2008 at 4:21pm6. 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 4:57pmWe 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!

- 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 -
**drwls**, Thursday, February 14, 2008 at 5:24pmSurely you meant to write cos 375 = cos 15

= cos (60 - 45)

- math -
- math(#1 of 6) -
**Jon**, Thursday, February 14, 2008 at 5:24pmin 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 5:30pmdrwls, 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 6:32pm60 + 45 is not 15

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