1. trig inequality

Hey everyone,

Thank you all for your help in the last few weeks.. It has been invaluable. I have been up since 10 last night and its now 5:30 in the morning, and I am still chugging away at the math.. I want to be able to mail it in before 12pm today when the post office closes.. Here are the last two I am having trouble with..

83) Find the regions where sinx <(or equal to) x

I can picture this easily, but I don't know how to write it..

84) State four points where cosx = (1/2)^x

I understand that the equal the same at 0 for 3pi/2.. Can't get any farther then that.. too tired =(

Please help! I promised my girlfriend I would be done the course and she's coming in the morning

2. Originally Posted by Slipery
Hey everyone,

Thank you all for your help in the last few weeks.. It has been invaluable. I have been up since 10 last night and its now 5:30 in the morning, and I am still chugging away at the math.. I want to be able to mail it in before 12pm today when the post office closes.. Here are the last two I am having trouble with..

83) Find the regions where sinx <(or equal to) x

I can picture this easily, but I don't know how to write it..

84) State four points where cosx = (1/2)^x

I understand that the equal the same at 0 for 3pi/2.. Can't get any farther then that.. too tired =(

Please help! I promised my girlfriend I would be done the course and she's coming in the morning
You're probably expected to use technology to solve these questions.

83) So one way is to draw the graph of y = sin x and y = x, get the x-coordinates of the intersection points and then state the intervals that satisfy $\displaystyle \sin x \leq x$.

84) Similar approach.

3. For the 2nd question..I have the graph and such, but how do I find the exact points of intersect..
The first will be (0,1), and the second is like (1.15, 0.5).. I am just estimating with that though

4. Q2. Using Wolfram Mathematica: In:=$\displaystyle \rm{FindRoot}[Cos[\it x]\rm == (1/2)^{\it x}\it , {x\rm , 100}]$ Out=$\displaystyle \{x\to 98.9602\}$;In:=$\displaystyle \rm{FindRoot}[Cos[\it x]\rm == (1/2)^{\it x}\it , {x\rm , 10}]$ Out:$\displaystyle \{x\to 10.9961\}$

5. Thanks!