Posted by **BreAnne** on Friday, April 13, 2012 at 2:02am.

can I please have help with these 3 questions?

1. Solve this equation graphically on the interval [0, 2ð]. list the solutions.

sin(2x)-1=tan x

2. solve sin x cos x= sqrt3/4

3. solve tan^2 x-3tan x+2=0

thank you! show step by step please.

- Trig -
**Reiny**, Friday, April 13, 2012 at 7:47am
1. try

http://www.wolframalpha.com/input/?i=sin%282x%29-1%3Dtan%28x%29+

2.

sinxcosx = √3/4

times 2

2sinxcosx = √3/2

sin(2x) = √3/2

2x = 60° or 2x = 120°

x = 30° or x = 60°

period of sin 2x is 180°

so other solutions

x = 30 + k(180) and x = 60 + k(180) degrees , where k is an inter

**in radians:
**

x = π/6 + kπ or x = π/3 + kπ

3. let tanx = t

you have t^2 - 3t + 2 = 0

(t-2)(t-1) = 0

t = 2 or t = -1

so

tanx = 2 -----> two answers in domain 0≤x≤2π

or

tanx = -1 ---> two answers in domain 0 ≤ x ≤ 2

give it a try

- Trig -
**BreAnne**, Saturday, April 14, 2012 at 11:04pm
thank you so much!

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