If tan(x) = -4/3, what is sin

I always do thes by deciding the correct quadrant

then draw the equivalent acute angle

Find the other side using pythagoras

Read the tan value off the triangle

Insert the correct sign.

The fraction -4/3 can be written either as -4/3 or 4/-3.

tan is defined to be opposite divided by adjacent or, when graphed, as y / x.

If you write the fraction as -4/3, then the y-value (opposite) is -4 and the x-value (adjacent) is 3. This point is in Quadrant IV. Using the Pytagorean Theorem, the hypotenuse becomes 5. To find the sin, use the formula for sin, which is opposite over hypotenuse:  sin(x) = -4/5.

If you write the fraction as 4/-3, the y-value is 4 and the x-value is -3, placing the angle in Quadrant II. The hypotenuse is again 5 and the sin becomes 4/5.

So, there are two possible answers.