Trig question

Question

Assume cos t = .45 and cos w = .89, both t and w are positive values between 0 and 2pi , and both t and w determine a terminal point in quadrant 4. Which of the following statements best describes the relationship between t and w?

 

A) t>2

B) w>t

C) not eough information

I chose b but I dont understand this question.

 

2.) If sin(theta)=4/5 and theta is in quadrant 2,the value of cot(theta) is...?

(Write as fraction if needed).

I don't understand this, but I tried.

 

If sin of theata=4/5, then I know the hypotenuse is 5.  I then assumed that this would be a 3,4,5 triagle.   Cot=cos(theta)/sin(theta).  I got 0.75. (3/4).

I don't know if 3/4 is correct.  Also, it's in quadrant 2...would that mean -3/4?  I am all over the grid lost here.  I tried to solve this problem but I really don't know how or what steps to take.  I'm not positive in my answer.  I feel like my answer is probably incorrect.

 

 

3.) if sin(theta)<0 and tan(theta)<0 then:

A) 0 degrees< theta<90 degrees

B) 90degrees<theta<180degrees

C) 180 degrees<theta<270degrees

D)270degrees<theta<360degrees

 

????  I don't understand this question!  

 

Please help!!!

Answer 1

Part 1

 

Find t and w.  Use the conditions and then compare t and w.  Remember that coterminal angles are 360°-t  for angle t and 360°-w for angle w.

 

Part 2
 
If you draw your right triangle, tangent will be opposite/adjacent = 4/3.  Then cotangent is 3/4 because you have to do the reciprocal.  You are on the right track so far.  Add the negative sign in front of 3/4 because tangent is negative in the second quadrant.  You answer here is -3/4.
 
Part 3
 
Sinθ is negative in the 3rd and 4th quadrant. Tanθ is negative in the 2nd and 4th quadrant.  Under these conditions, the quadrant they have in common is the 4th quadrant.  So your answer is D.