Question

I need help with this practice problem solving My attempted answer is in the picture, though I don’t know if I’m correct, that’s why I’m checking

Answer 1

Given:

Given that a trigonometric statement.

Required:

To check whether the given statements are true or false`.

Step-by-step explanation:

(1)

Now consider LHS side of the given statement,

`\cos(-(5\pi)/(3))=\cos(2\pi-(5\pi)/(3))`

Because adding 2π does not change the value of a trigonometric function.

Now,

`\begin{gathered} \cos(2\pi-(5\pi)/(3))=\cos(\pi)/(3) \\ \\ =(1)/(2) \end{gathered}`

Therefore, the statement is false.

(2)

`\begin{gathered} cot(-(11\pi)/(3))=cot(\pi)/(3) \\ \\ =(1)/(√(3)) \end{gathered}`

Therefore, the statement is False.

(3)

Remove full rotations of 2π until the angle is between 0 and 2π.

`\begin{gathered} \sin((27\pi)/(2))=\sin((3\pi)/(2)) \\ \\ =-1 \end{gathered}`

Therefore, the statement is TRUE.

Final Answer:

The first and second statement are FALSE and the third one is TRUE.

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