# Trigonometry inequality

#### Clara Chung

1. The problem statement, all variables and given/known data
show that 1-t^2/2 <=cos(t) <=1 for 0<=t<=1

2. Relevant equations
Trigonometry knowledge

3. The attempt at a solution
I don't know how to relate t with cos(t), and I also try to find out cos(1), but there is no result, so how can I start with this problem.

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#### SammyS

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1. The problem statement, all variables and given/known data
show that 1-t^2/2 <=cos(t) <=1 for 0<=t<=1

2. Relevant equations
Trigonometry knowledge

3. The attempt at a solution
I don't know how to relate t with cos(t), and I also try to find out cos(1), but there is no result, so how can I start with this problem.
Are you sure that it's 0 ≤ t ≤ 1 , and not 0 ≤ t ≤ π/2 ?

#### Clara Chung

Yes, this is what the question said. How can you solve for 0 <= t <= pi/2 ?

#### Clara Chung #### Mark44

Mentor
show that 1-t^2/2 <=cos(t) <=1 for 0<=t<=1
Have you know about Maclaurin series yet, and in particular, the Maclaurin series for cos(t)?

From another question you posted, you are taking a calculus class. If so, both questions should have been posted in the Calculus & Beyond section, not the Precalculus section.

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