Question

The figure below shows a rectangle with a diagonal drawn.

Which equation shows the trigonometric relationship between complementary angles?
A.sin(t) = sin(u)
B.sin(s) = cos(u)
C.cos(s) = sin(v)
D.cos(t) = cos(v)

Answer 1

Answer: B

Step-by-step explanation: I took the test

Answer 2

Option B. sin(s) = cos(u)

Explanation:

The rest of the question is the attached figure.

Complementary angles - two angles that add to 90 degrees.

The sine of one of them will be equal to the cosine of other angle.

For the attached figure:

The set all complementary angles are:

1. angle s and angle t
2. angle u and angle v
3. angle s and angle u
4. angle t and angle v

We will check the options:

A. sin(t) = sin(u) ⇒(wrong) because t and u are not complementary angles

B. sin(s) = cos(u) ⇒ (True) ⇒ s and u are complementary angles and sine of one of them will be equal to the cosine of other angle.

C. cos(s) = sin(v) ⇒(wrong) because t and u are not complementary angles

D. cos(t) = cos(v) ⇒(wrong) because t and v are complementary angles but sine of one of them should be equal to the cosine of other angle.

The answer is option B. sin(s) = cos(u)