Expert: Jack Cheng - 1/1/2007

Question
I had a long trig review packet to do over Christmas break. I have completed most of the questions and was wondering if you could please confirm that some of my answers are correct.

If it is possible to express answers in exact form, you are expected to do so. If exact answers are not possible, round to the nearest tenth of a degree or nearest hundredth of a radian (whichever unit measure the question calls for).

1) Q: Solve for all values of x: sinx=-1 (in radians).
  A: x= 3pi/2 + n times 2pi (Let n= an integer)

2) Q: Find the exact value of tan 105 degrees.
  A: -2 + square root of 3

3) Q: If pi/2 < x < pi and sinx=5/13, find sin 2x.
  A: 120/169 (I tried to reduce it and can't)

4) Q: Find the exact value of csc 300 degrees.
  A: -2 square root of 3 divided by 3

5) Q: Find the exact value of tan(Cos^-1(-square root of 3 divided by 2)).
  A: -square root of 3 divided by three

11)Q: If tan A=2 and tan B= 1/4, find tan(A-B).
  A: 7/6    or    1 and 1/6 (I'm not sure which is more simple)

12) Q: Find the exact value: cos (5pi/12) cos (pi/6) + sin (5pi/12) sin (pi/6)
   A: Square root of 2 divided by 2

Answer
Hi Karen,

1) Correct!

2) It can't be right. Do it on a calculator; they don't even come close. I got [1+sqrt(3)]/[1-sqrt(3)].

3) You're right. 120/169 is reduced fully.

4) Right again!

5) Right again!

11) I would prefer 7/6, but both are fine. One is an improper fraction and the other a mixed number; neither is simpler than the other.

12) This is correct, again.

Good job, you only missed one. That's very good. :)

~ Jack