Thread: Homework Help!! exact value, -pi < θ ≤ pi

1. Homework Help!! exact value, -pi < θ ≤ pi

Hi All,

Could somebody please explain (step by step) how to find the exact value of sinx= -1/√2 when -pi < θ ≤ pi? Been trying to google but the only example is between 0 < θ ≤ 2pi..

Many thanks

2. Re: Homework Help!! exact value, -pi < θ ≤ pi

Get the solutions for the easy region, then add multiples of 2pi until you have all the solutions in the region you are given.

3. Re: Homework Help!! exact value, -pi < θ ≤ pi

$\text{Disregard the minus sign temporarily and put} \\ \\ sin^{-1} \frac{1}{\sqrt{2}} \\ \\ \text{in your calculator, this will give you the reference angle of 45 or} \ \frac{\pi}{4} \\ \\ \text{The sine is negative in 3rd and 4th quadrants so your 2 solutions will be} \\ \\ - \pi \ + \ \frac{\pi}{4} \ = \ - \frac{3 \pi}{4} \\ \\ and \\ \\ - \frac{\pi}{4}$

4. Re: Homework Help!! exact value, -pi < θ ≤ pi

Originally Posted by agentmulder
$\text{Disregard the minus sign temporarily and put} \\ \\ sin^{-1} \frac{1}{\sqrt{2}} \\ \\ \text{in your calculator, this will give you the reference angle of 45 or} \ \frac{\pi}{4} \\ \\ \text{The sine is negative in 3rd and 4th quadrants so your 2 solutions will be} \\ \\ - \pi \ + \ \frac{\pi}{4} \ = \ -3 \frac{\pi}{4} \\ \\ and \\ \\ - \frac{\pi}{4}$
I'm sure you mean $\displaystyle -\frac{3\pi}{4}$...

5. Re: Homework Help!! exact value, -pi < θ ≤ pi

Yes, i guess the way i wrote it the fraction looked like a mixed number, i edited the post.

6. Re: Homework Help!! exact value, -pi < θ ≤ pi

Keep in mind that the sin(-x) = -sinx

Howard Heller
InteractiveMathTutor.com

7. Re: Homework Help!! exact value, -pi < θ ≤ pi

Originally Posted by IMTinstructor
Keep in mind that the sin(-x) = -sinx

Howard Heller
InteractiveMathTutor.com
Anyone stupid enough to fall for you scam deserves the outcome.
I can find no entry for you at MathGenealogy Project

So what equips you to tutor?

8. Re: Homework Help!! exact value, -pi < θ ≤ pi

What equips me to tutor? First of all, equips is not english to you must be from another country. I though am from the United States. Lets see... Math major, expert in math, actuary science major, mba, etc etc.