Question

1. Find the complete exact solution of sin x = .
2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to
two decimal places.
3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two
decimal places.

4. Prove that tan2  – 1 + cos2  = tan2  sin2 .
5. Prove that tan  sin  + cos  = sec .
6. Prove that = cos  + sin .
7. Prove that .
8. Prove that = cos  – cot  cos .
9. Find a counterexample to shows that the equation sec  – cos  = sin  sec  is not
an identity.
sin cos
tan sin cos tan
2 2 ω ω
ωω ω ω
−
+
1 + tan
1 tan
sec + 2tan
1 tan
2
2
θ
θ
θ θ
− − θ
=
tan cos + sin
sin

10. Write tan as a function of  only.
11. Write cos as a function of  only.
12. Write cos(–83°) as a function of a positive angle.
13. Write sin(125°) in terms of its cofunction. Make sure your answer is a function
of a positive angle.
14. Find the exact value of sin(195°).

Answer 1

no ideas on any of these? Also you have some major typos and/or formatting issues.

I'll do a couple. Maybe you can clean up the post and indicate where you get stuck on the others.

#2
cos 2x – 3sin x cos 2x = 0
(1-3sinx)cos2x = 0
so, either
cos2x=0 ==> x = pi/4 or 3pi/4
sinx = 1/3 ==> x=arcsin(1/3) or pi-arcsin(1/3)

#3
tan2 x + tan x – 1 = 0
tanx = (-1±√5)/2
so find arctan of those two values and recall that tan is positive in QI,QIII and negative in QII,QIV

Answer 2

alright, I will. Thanks