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\\eq 1`

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

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