# MAT - Paper 2011 - Q1I

> Source: https://ollybritton.com/notes/maths/problems/mat/2011/q1i/ · Updated: 2021-08-09 · Tags: maths, mat, notes

## Flashcards
##### When is $y^2 < y$??
For $0 < y < 1$.

##### Why does $\sin^8(x) + \cos^6(x)$ have to be less than $\sin^2(x) + \cos^2(x)$ for $0 < y < 1$??
Because $\sin(x)$ and $\cos(x)$ are between $1$ and $0$, so squaring them can only make them smaller.

##### How can you determine the number of solutions to $\sin^8(x) + \cos^6(x) = 1$??
This can only happen when $\sin^2(x) = 1$ and $\cos^2(x) = 0$ or vice versa because of how squaring works.

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