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 C
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 don't know 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
6 answers
2) Wrong. (1-csc^2x)/cot^2x
= [(sin^2x-1)/sin^2x]*sin^2x/cos^2x
= -cos^2/cos^2 x = -1
3) Wrong. -5(cot^2x - csc^2 x)
= -5(cos^2x -1)/sin^2x
= -5(-sin^2x/sin^2x)= +5
4) Correct. Sec^2 is always 1 or greater. Adding tan^2 makes it even larger.
Please show your work on the others, so we can see where you are making your other mistakes.
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.
You are not going to learn the subject if someone else does all the problems for you. Please post the problems one at a time and go through as many stps as you can. You need to review the subjects of trigonometric identities and the signs of trig functions in the various quadrants. Drawing a figure is a big help.