Just would like to know the answer to this question.

Question

What conjecture can you make about the tangent of complementary angles?

Answer 1

As a hint: it might help to draw a right triangle, label the three sides (using a, b, and c, for example), and calculate the tangent for the two non-right angles in the triangle. These will automatically be complementary angles, since (if we label them as A and B) we have A + B + 90 = 180, which simplifies to A + B = 90.

Once you calculate tan(A) and tan(B), you can compare these two expressions and see how they're related.

Answer 2

Angles A and B are complementary if A+B =90 degrees = pi/2

A=90-B

tanA = tan(90-B) = 1/tanB

tanA = 1/tanB

tanB = 1/tanA

the tangents of complementary angles are inverses of each other

for example

tan30 = 1/sqr3 = 1/tan60

tan60=sqr3 = about 1.732

tan30 =1/sqr3 = about 0.577

1/.577 = 1.732

1/1.732 = .577

tan60 = sqr3 = 1/tan30

if tanA = 200, then tanB = 1/200

if tanA = x, then tanB = 1/x

these are not just "conjectures," these are identities, equations that are always true regardless of the values of A and B, as long as A+B = 90 degrees or pi/2, and 0 < A, B, < 90