How do you square $\sin θ\,$? Is $(\sinθ)^2=\sin^2θ$
or
$(\sinθ)^2=\sin(θ^2)$
or
$(\sinθ)^2=\sin^2(θ^2)$
Can you explain your answer, regards Tom. Also, does your answer work for $\cos$ and $\tan$?
 A: $$(\sin \theta)^2=\sin^2 \theta.$$
Nothing to add
A: Hint: $\sin^2 \theta + \cos^2 \theta =1$ means $(\sin \theta)^2 + (\cos \theta)^2 = 1$. This thing is repeated so often that it becomes $\sin^2 + \cos^2 = 1$ (for all arguments). That's one reason why $\sin^2 \theta$ is written instead of the more pedantic $(\sin \theta)^2$. 
A: In general, we write $(\sin \theta)^2$ as $\sin^2 \theta$. The same is true for cosine and tangent.
A: $(\sin \theta)^2$ is the square of the sine of $\theta$
.  Traditionally (but some people say illogically), $\sin^2 \theta$ also means this.
If you want $\sin(\theta^2)$ it is best to use parentheses.
A: Def: $\sin^2 \theta$ =  $ (\sin\theta)^2$. 
If you need motivation for why we define it that way, recall the geometric definitions of sin and cos: 

So consider the following now: 
$\sin^2 \theta$ + $\cos^2 \theta$ = $(\frac {x}{r})^2$ +  $(\frac {y}{r})^2$ = $(\frac {x^2 + y^2}{r^2})$ = $(\frac {r^2}{r^2})$ = 1. 
This is false if we assume  $ (\sin\theta^2)$ or $(\cos\theta^2)$. So this definition gives much simpler trigonometric relations. 
A: $(...)^2$ is a square of some number. So you first get the number then square it. $\sin(\theta^2)$ is a sine of something's square.
A: Here are some numbers to crunch
If you were to believe that 
A) $(\sinθ)^2=\sin^2θ$ is true, which it is.
Lets plug in $\theta=30^\circ$, so 
$\sin 30^\circ=\frac{1}{2}$
Then it becomes just another value, which need be squared. So, it becomes $\frac{1}{4}$
Let's look at 
B) $(\sinθ)^2=\sin(θ^2)$.
If we plug in $\theta=30^\circ$, we are implying that $(\sinθ)^2=\sin (30^2)^\circ=\sin 900^\circ=0.99$
C) is an extension of B) which is just square of 0.99.
Overall, what I want to imply is these are all trigonometric ratios, they yield a certain value and they are treated like any other ratio. 
