Here, we have drawn a right triangle (with sides 3, 4 and 5) in each of the 4 quadrants.
Since all 6 trigonometric functions are positive in the first quadrant , let's look at the green triangle in quadrant II.
How can we tell if the sine function is postive or negative in the second quadrant?
• The sine function equals the opposite side (yvalue) divided by the hypotenuse. As we can see the yvalue is positive and so the sine value is positive.
• The cosine function equals the adjacent side (xvalue) divided by the hypotenuse. The adjacent side is negative and therefore the cosine value is negative.
• The tangent function equals the opposite side (yvalue) divided by the adjacent side (xvalue). Even though the opposite side is positive, the adjacent side is negative and therefore the tangent value is negative.
• cotangent function = adjacent side (xvalue) ÷ opposite side (yvalue).
adjacent side is negative, therefore cotangent is negative.
• secant function = hypotenuse ÷ adjacent side (xvalue).
adjacent side is negative, therefore secant is negative.
• cosecant function = hypotenuse ÷ opposite side (yvalue).
opposite side (yvalue) is positive therefore cosecant is positive.
You can easily determine these for the other quadrants.
