Posted by **suzy ** on Friday, August 16, 2013 at 4:53pm.

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°).

- trig help much appreciated! :)) -
**Steve**, Friday, August 16, 2013 at 4:58pm
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

- trig help much appreciated! :)) -
**Suzy**, Friday, August 16, 2013 at 6:37pm
alright, I will. Thanks

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