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

Question

asked Jan 1, 2021 10.0k views

1 Answer

Tgrrr · Answer 1 · 2021-01-04T23:10:14+0000

Recall the fundamental rule of trig:

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

So, there exists an angle
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

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

So, there doesn't exist a number
such that

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