Question

Write the following expression as a function of a positive acute angle. Use "+" to indicate a positive value and "-" to indicate a negative value.

Answer 1

Since the trigonometric functions are periodic, we know that

`\cos(x)=\cos(x+360)`

In this case, you have

`\cos(-240)=\cos(-240+360)=\cos(120)`

Finally, we have

`\cos(120)=\cos(90+30)`

and you can use the formula

`\cos(90+x)=-\sin(x)`

To conclude

`\cos(120)=\cos(90+30)=-\sin(30)`

Answer 2

As property of trigonometric cosine function, we have:

cos(x) = cos(-x)

=> cos(-240) = cos(240)

Otherwise, we also have:

cos(x + 180) = -cos(x)

=> cos(240) = - cos(60)

=> cos(-240) = cos(+240) = -cos(+60)

Hope this helps!

:)