trig (1 Viewer)

[fullonoob]

Prove algebraically that if n is a solution of the equation 2cosx = 1 - .5x, then -2 <_n<_6.

when showing this graphically is the negative solution(3 solutions) on the left of y axis or right of y axis. The answer at the back of book says on the left, but that is above the x axis meaning y>0 so not negative? is it incorrect? or does it relate to the ASTC theory where 2nd quad is negative

 

[Trebla]

Prove algebraically that if n is a solution of the equation 2cosx = 1 - .5x, then -2 <_n<_6.

when showing this graphically is the negative solution(3 solutions) on the left of y axis or right of y axis. The answer at the back of book says on the left, but that is above the x axis meaning y>0 so not negative? is it incorrect? or does it relate to the ASTC theory where 2nd quad is negative

If x = n satisfies this equation then:
2cos n = 1 - 0.5n
But
- 1 ≤ cos n ≤ 1
=> - 2 ≤ 2cos n ≤ 2
=> - 2 ≤ 1 - 0.5n ≤ 2
=> - 3 ≤ - 0.5n ≤ 1
.: - 2 ≤ n ≤ 6

 

[fullonoob]

you is the pro

 

[hscishard]

Wow. Nice man

 

[Imaginaryfriend]

Good job

I like your Display picture