Is this true or false? sin^2(θ) ≠ sin(θ)^2

Don't understand this hw questions.. I believe it is false though?

3 Answers
Apr 6, 2018

I would answer that it is true.

Explanation:

This hw question is a question about notation.

${\sin}^{2} \left(\theta\right)$ is the same as ${\left(\sin \left(\theta\right)\right)}^{2}$

I would read $\sin {\left(\theta\right)}^{2}$ as equivalent to $\sin \left({\theta}^{2}\right)$

(But I've noticed that WolframAlpha treats $\sin {\left(\theta\right)}^{2}$ as equal to ${\left(\sin \left(\theta\right)\right)}^{2}$.

I would never write $\sin {\left(\theta\right)}^{2}$ because it is ambiguous.

Apr 6, 2018

True.

Explanation:

${\sin}^{2} \left(\theta\right) \ne \sin {\left(\theta\right)}^{2}$

If you read $\sin {\left(\theta\right)}^{2}$ as $\sin \left({\theta}^{2}\right)$ then the statement is true.

${\sin}^{2} x$ is the square of a ratio.

$\sin \left({x}^{2}\right)$ is the square of an angle.

Apr 6, 2018

True, ${\sin}^{2} \left(\theta\right) \ne \sin {\left(\theta\right)}^{2}$

Here's how I did it:

Explanation:

If you do $\sin {\left(x\right)}^{2}$, that means you are squaring the angle, instead of the value of $\sin \left(x\right)$. For example:

$\sin {\left({30}^{\circ}\right)}^{2} = \sin \left({900}^{\circ}\right) = \sin \left({180}^{\circ}\right) = 0$
is different from
${\sin}^{2} \left({30}^{\circ}\right) = {\left(\frac{1}{2}\right)}^{2} = \frac{1}{4}$

Therefore, ${\sin}^{2} \left(\theta\right) \ne \sin {\left(\theta\right)}^{2}$.

The answer is true .

Hope this helps!