Why do cosine and secant have the same sign in all quadrants?

[HussanAli]

Identifying the signs of ratio in four quadrants. It turns out that -ive trignometric identity will be negative but not for cos and sec. But why?

 

[rock.freak667]

if you mean why cos(-x)=cos(x)

is because if you draw x clockwise,it lies in the 4th quadrant and where is cos(x) +ve?

 

[tomcue]

This is because cosine and secant are even functions, meaning that they have the same value regardless of whether the angle is positive or negative. Therefore, the signs of these ratios do not change in different quadrants. However, sine and tangent are odd functions, meaning that their values change when the angle is negative. This is why their signs change in different quadrants. It is important to understand these sign changes in order to accurately use trigonometric ratios in various mathematical and scientific applications.