Question

There are values of t so that sin t=.35 and cos t=.6

Answer 1

Recall the fundamental rule of trig:

$\sin^2(x)+\cos^2(x)=1 \quad\forall x \in \mathbb{R}$

So, there exists an angle $t$ such that

$(0.6,0.35)=(\sin(t),\cos(t))$

if and only if

$\sin^2(t)+\cos^2(t)=0.6^2+0.35^2=1$

Working out the numbers, we get

$0.6^2+0.35^2=0.36+0.1225=0.4825\neq 1$

So, there doesn't exist a number $t$ such that

$(0.6,0.35)=(\sin(t),\cos(t))$