Trigonometry Practice

Find sin A if cos A =7/25

I. Quadrant:

\(\sin{(A)} = + \sqrt{1-\cos^2{(A)}}\\ \sin{(A)} = + \sqrt{1-(\frac{7}{25})^2}\\ \sin{(A)} = + \sqrt{1-\frac{7^2}{25^2}}\\ \sin{(A)} = + \sqrt{ \frac{25^2-7^2}{25^2}}\\ \sin{(A)} = + \frac{ \sqrt{ 25^2-7^2 } } {25}\\ \sin{(A)} = + \frac{24} {25}\\ \sin{(A)} = 0.96\)

IV. Quadrant:

\(\sin{(A)} = - \sqrt{1-\cos^2{(A)}}\\ \sin{(A)} = -\sqrt{1-(\frac{7}{25})^2}\\ \sin{(A)} = - \sqrt{1-\frac{7^2}{25^2}}\\ \sin{(A)} = - \sqrt{ \frac{25^2-7^2}{25^2}}\\ \sin{(A)} = - \frac{ \sqrt{ 25^2-7^2 } } {25}\\ \sin{(A)} = - \frac{24} {25}\\ \sin{(A)} = -0.96\)

sin(A)=24/25

use sin(A)^2+cos(A)^2=1

or 7^2+24^2=25^2

ok I think I get it thanks