Trigonometric Equations ( confused)

[killasnake]

Hi I am just sooo confused and I don't know what to do... or even start Can someone please explain this.

The smallest positive number for which

3sin(2x-6)=1

is X= ______


and

3sin(2x-5)=1


and

4cos^2 x-9cosx+2=0


I really don't know how to do these.

 

[Guest]

3sin(2x-6)=1


sin y = 1/3 where y= (2x-6)



4cos^2 x-9cosx+2=0

4p^2 -9p + 2= 0 where p = cos x

solve the quadratic and then sub it into p =cos x

 

[soroban]

Hello, killasnake!

The first two are basic Algebra ... with one trig step thrown in . . .

Find the smallest positive number for which: .\(\displaystyle 3\cdot\sin(2x\,-\,6) \:= \:1\)

We are given: . . . . . . \(\displaystyle 3\cdot\sin(2x\,-\,6)\;=\;1\)

Divide both sides by 3: . \(\displaystyle \sin(2x\,-\,6) \:= \:\frac{1}{3}\)

Take the inverse sine: . . . . . .\(\displaystyle 2x\,-\,6 \:= \:\sin^{-1}\left(\frac{1}{3}\right)\)

Add 6 to both sides: . . . . . . . . . . .\(\displaystyle 2x \:= \:\sin^{-1}\left(\frac{1}{3}\right)\,+\,6\)

Divide both sides by 2: . . . . . . . . . .\(\displaystyle x \:= \:\frac{1}{2}\cdot\sin^{-1}\left(\frac{1}{3}\right)\,+ \,3\)

With my calculator in <u>radian</u> mode, I get: .\(\displaystyle x \:\approx \:3.17\)

 

[killasnake]

Oh.... Okay I got it now Thank you for the help.