Question

Which relationship in the triangle must be true?

A) sin(B) = sin(A)
B) sin(B) = cos(90 – B)
C) cos(B) = sin(180 – B)
D) cos(B) = cos(A)

Answer 1

We'll assume this is an arbitrary triangle ABC.

A) No, the sines of two different angles can be whatever they want

B) sin(B)=cos(90-B)

Yes, that's always true. The "co" in cosine means "complementary" as in the complementary angle, which adds to 90. So the sine of an angle is the cosine of the complementary angle.

C) No, the correct identity is sin(180-B)=sin B. Supplementary angles share the same sine.

D) Just like A, different triangle angles often have different cosines.

Answer: Choice B