Given cot A = 3 over 7 and that angle A is in Quadrant I, find the exact value of cos A in simplest radical form using a rational denominator

Answer 1

cot is adjacent/opposite. Therefore:

adjacent = 3

opposite = 7

cos is adjacent./hypotenuse. We can use the Pythagorean theorem to find the hypotenuse.

a²+b²=c²

3²+7²=c²

9+49=c²

58=c² Take the square root of both sides

√58=c

cos = 3/√58 To rationalize, multiply the numerator and denominator by √58

cos = (3/√58)(√58/√58) = 3√58/58