what is the complementary angle of 13pi/37?

Complementary angles combine to form a right angle (90° or π/2 radians)

So to find the complementary angle, subtract from π/2:

π/2 - 13π/37

Get a common denominator of 74:

(37/37) * π/2 - (2/2) * 13π/37

= 37π/74 - 26π/74

Now subtract the numerators:

(37π - 26π) / 74

= 11π / 74

(pi/2 - 913pi/37) = -(1789 π)/74

pi - 13pi/37 =>

24pi/37 is the complementary angle

Complementary angles add up to 90°.  In terms of radians, this is (1/2)π radians.

So if we have the complementary angle an unknown "x", we can set up an equation that we can solve:

(13/37)π + x = (1/2)π

Multiply both sides by 74 to get rid of the fractions:

26π + 74x = 37π

Subtract 26π from both sides:

74x = 11π

Divide both sides by 74:

x = (11/74)π radians.