### Home > APCALC > Chapter 9 > Lesson 9.2.1 > Problem9-53

9-53.

No calculator! Determine all point(s) of intersection of $y = 3\cos(x)$ and $y = 2\cos^2(x) + 1$ over the interval $0 ≤ x ≤ 2π$.

$3\cos(x)=2\cos^2(x)+1$

$0=2\cos^2(x)-3\cos(x)+1$

$0=(2\cos(x)-1)(\cos(x)-1)$

$2\cos(x)-1=0\text{ or }\cos(x)-1=0$

Solve the equations in Step 4. Note that these solutions only give the $x$-values. The problem asks for the "points", so you need to calculate the corresponding $y$-values.