cos inverse of -0.28 (1 Viewer)

[sssona09]

is it the same as cos inverse 0.28? how does the minus sign affect things and how can I visualise this using quadrants and stuff

thank you

 

[fan96]

No.

Let (where arccos is the inverse cosine function)

If as you suggested, then it would follow that . Therefore, .

But this can't be true because the cosine function is a function.

As a real example,

 

[sssona09]

ah thank you!!

 

[fan96]

However, it is true that (the cosine function is even), and (the sine function is odd).

You can flip any angle across the x-axis to change its sign.

S | A
T | C
______________________________________________

Let's bold the quadrants in which is positive.

S | A
T | C

The cosine function represents the horizontal length of the triangle formed at that point on the unit circle. So the magnitude of the cosine function will be the same even if you reverse the sign of the angle.

For any angle you choose on the unit circle, reversing its sign and flipping it across the x-axis will not change the sign of the cosine function.

So if neither the magnitude nor the sign of the cosine function is changed by reversing the sign of the angle, it follows that .
______________________________________________

Now, let's bold the quadrants in which is positive.

S | A
T | C

The sine function represents the vertical height of the triangle formed at that point on the unit circle. So, again, the magnitude of the sine function will be the same even if you reverse the sign of the angle.

For any angle you choose on the unit circle, reversing its sign and flipping it across the x-axis will ALWAYS change the sign of the sine function.

So if magnitude does not change but the sign always does, it follows that .