Question

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

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

Answer 1

I would answer that it is true.

Explanation:

This hw question is a question about notation.

`sin^2(theta)` is the same as `(sin(theta))^2`

I would read `sin(theta)^2` as equivalent to `sin(theta^2)`

(But I've noticed that WolframAlpha treats `sin(theta)^2` as equal to `(sin(theta))^2`.

I would never write `sin(theta)^2` because it is ambiguous.

Answer 2

True.

Explanation:

`sin^2(theta)!=sin(theta)^2`

If you read `sin(theta)^2` as `sin(theta^2)` then the statement is true.

`sin^2x` is the square of a ratio.

`sin(x^2)` is the square of an angle.

Answer 3

True, `sin^2(theta) != sin(theta)^2`

Here's how I did it:

Explanation:

If you do `sin(x)^2`, that means you are squaring the angle, instead of the value of `sin(x)`. For example:

`sin(30^@)^2=sin(900^@) = sin(180^@) = 0`
is different from
`sin^2(30^@) = (1/2)^2 = 1/4`

Therefore, `sin^2(theta) != sin(theta)^2`.

The answer is true .

Hope this helps!