Question

solve $\cos(x)=0.84$ on $0\leq x<2\pi$.
there are two solutions, a and b, with $a < b$.
$a = $
$b = $
give your answers accurate to 3 decimal places.
question help: video post to forum

Explanation:

Step1: Find the first solution

We know that if $\cos(x) = a$, then $x=\cos^{-1}(a)+2k\pi$ or $x = 2\pi-\cos^{-1}(a)+2k\pi$ for $k\in\mathbb{Z}$. For $a = 0.84$ and $k = 0$, the first solution $A=\cos^{-1}(0.84)$. Using a calculator, $A=\cos^{-1}(0.84)\approx0.589$.

Step2: Find the second solution

The second - solution $B = 2\pi-\cos^{-1}(0.84)$. Since $\pi\approx3.142$, then $B=2\times3.142 - 0.589=6.284 - 0.589 = 5.695$.

Answer:

$A = 0.589$
$B = 5.695$