Question

Use a graphing utility to solve the equation on the interval 0°< x < 360°. Express the solution(s) rounded to one decimal place.

cos^2 x + cos x - 1 = 0

Answer 1

first find the value of cos(x) by solving the given equation.

Answer 2

Substitute y = cos x, then y^2 + y -1=0. By quadratic formula, \[y=\frac{-1 \pm \sqrt5}{2}=\cos x\]Only the plus (of the plus or minus) will work, since the absolute value of cos x is never more than one. The arccos function will give you angles that correspond to the value of cos x.

Answer 3

go and download geogebra http://www.geogebra.org/cms/ this will allow you to graph the curve... as the question asks. The solutions will be where the curve cuts the x-axis

Answer 4

im still not understanding

Answer 5

i already download that

Answer 6

say y = cosx

then your equation will become
y^2+y-1=0

graph this equation.

Answer 7

ok... the only problem is that it will give the decimal values... and you will need to set the x-axis scale to radians...

Answer 8

type your function into geogebra as

\[f(x) = (\cos(x)^2 + \cos(x) - 1\]

then use the roots function

\[roots[f, 0, 2\pi]\]

it will show the roots as points... but only as a decimal...

an alternative would be wolfram alpha which would probably give exact values.

http://www.wolframalpha.com/

Answer 9

oopps the function should be

\[f(x) = (\cos(x))^2 + \cos(x) - 1\]

Answer 10

i still not have the solution lol

Answer 11

i graph it but i dont see any number

Answer 12

ok... do you see a any points A, B, C, etc..?

Answer 13

nope there is no abc

Answer 14

hold on...

Answer 15

the error in your curve is that

you need to enter cos^2(x) as (cos(x))^2 this will give the correct curve

Answer 16

f(x)=(cos(x))^2+cos(x)−1?

Answer 17

here is my graph

Answer 18

thats correct...

Answer 19

so once you have that you will need to use the roots command

for the start and end value of the curve just use zero and 7

so the command is

roots[f,0,7]

and the points A and B should appear...

Answer 20

and then in the algebra window you'll have a decimal approximation.

Answer 21

http://www.wolframalpha.com/input/?i=cos^2+x+%2B+cos+x+-+1