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

I Need Help With This Practice Problem Solving My Attempted Answer Is In The Picture Though I Dont Know If Im Correct Thats Why Im Checking class=

Answer :

Given:

Given that a trigonometric statement.

Required:

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

Explanation:

(1)

Now consider LHS side of the given statement,

[tex]\cos(-\frac{5\pi}{3})=\cos(2\pi-\frac{5\pi}{3})[/tex]

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

Now,

[tex]\begin{gathered} \cos(2\pi-\frac{5\pi}{3})=\cos\frac{\pi}{3} \\ \\ =\frac{1}{2} \end{gathered}[/tex]

Therefore, the statement is false.

(2)

[tex]\begin{gathered} cot(-\frac{11\pi}{3})=cot\frac{\pi}{3} \\ \\ =\frac{1}{\sqrt{3}} \end{gathered}[/tex]

Therefore, the statement is False.

(3)

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

[tex]\begin{gathered} \sin(\frac{27\pi}{2})=\sin(\frac{3\pi}{2}) \\ \\ =-1 \end{gathered}[/tex]

Therefore, the statement is TRUE.

Final Answer:

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

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