Nov 11, 2012 Thread starter #1 M melissax New member Nov 11, 2012 8 Hello, I have some questions and i couldnt solve them can you help me? If y=5cos(x)+3 then what is the heap of ? (a) All real numbers (b) alpha<= y <= alpha (c) -2 <= y <= 10 ( d)-2 <= y <= 8 What is the solution? Thank you. Last edited by a moderator: Feb 21, 2013
Hello, I have some questions and i couldnt solve them can you help me? If y=5cos(x)+3 then what is the heap of ? (a) All real numbers (b) alpha<= y <= alpha (c) -2 <= y <= 10 ( d)-2 <= y <= 8 What is the solution? Thank you.
Nov 11, 2012 Admin #2 M MarkFL Administrator Staff member Feb 24, 2012 13,775 re: Finding the Range of a Trignometric Function To find the range of the given sinusoid, I would use this method: $\displaystyle -1\le\cos(x)\le1$ $\displaystyle -A\le A\cos(x)\le A$ $\displaystyle B-A\le A\cos(x)+B\le B+A$ Can you apply this procedure to the function you are given?
re: Finding the Range of a Trignometric Function To find the range of the given sinusoid, I would use this method: $\displaystyle -1\le\cos(x)\le1$ $\displaystyle -A\le A\cos(x)\le A$ $\displaystyle B-A\le A\cos(x)+B\le B+A$ Can you apply this procedure to the function you are given?
Nov 11, 2012 Thread starter #3 M melissax New member Nov 11, 2012 8 re: Finding the Range of a Trignometric Function Thank you very much You showed me path, i will apply.
re: Finding the Range of a Trignometric Function Thank you very much You showed me path, i will apply.
Nov 11, 2012 Thread starter #4 M melissax New member Nov 11, 2012 8 re: Finding the Range of a Trignometric Function -1<=5*Cos(x)+3<=1 -5<=5*Cos(x)+3<=5 -5-3<=5Cos(x)<=5-3 -8<=5Cos(x)<=2 As i understand between -2 and 8 but how i can show?
re: Finding the Range of a Trignometric Function -1<=5*Cos(x)+3<=1 -5<=5*Cos(x)+3<=5 -5-3<=5Cos(x)<=5-3 -8<=5Cos(x)<=2 As i understand between -2 and 8 but how i can show?
Nov 11, 2012 Admin #5 M MarkFL Administrator Staff member Feb 24, 2012 13,775 re: Finding the Range of a Trignometric Function You have found the correct range, but what you actually want to do is this: Begin with the fact that the cosine function varies from -1 to 1: $\displaystyle -1\le\cos(x)\le1$ Multiply through by the given amplitude of 5: $\displaystyle -5\le 5\cos(x)\le5$ Add through by the given vertical displacement of 3: $\displaystyle 3-5\le 5\cos(x)+3\le3+5$ Simplify: $\displaystyle -2\le 5\cos(x)+3\le8$ And this demonstrates the range is [-2,8].
re: Finding the Range of a Trignometric Function You have found the correct range, but what you actually want to do is this: Begin with the fact that the cosine function varies from -1 to 1: $\displaystyle -1\le\cos(x)\le1$ Multiply through by the given amplitude of 5: $\displaystyle -5\le 5\cos(x)\le5$ Add through by the given vertical displacement of 3: $\displaystyle 3-5\le 5\cos(x)+3\le3+5$ Simplify: $\displaystyle -2\le 5\cos(x)+3\le8$ And this demonstrates the range is [-2,8].
Nov 11, 2012 Thread starter #6 M melissax New member Nov 11, 2012 8 re: Finding the Range of a Trignometric Function I am sory. You showed me path but i wrote wrong. When i solved second then i saw? Thank you. You are great teacher.
re: Finding the Range of a Trignometric Function I am sory. You showed me path but i wrote wrong. When i solved second then i saw? Thank you. You are great teacher.
Nov 11, 2012 Admin #7 M MarkFL Administrator Staff member Feb 24, 2012 13,775 re: Finding the Range of a Trignometric Function Glad to help out, and welcome to the forum!