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°).
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