The relationship between the sine and cosine of ∠A and the sine and cosine of ∠B for given angles, sin(A) = cos(B) and
sin(B) = cos(A)
"Two or more angles are complementary if their sum is 90° "
For given question,
∠A and ∠B are complementary angles.
⇒ ∠A + ∠B = 180°
For ∠A = 15° the measure of ∠B is 75°
For ∠A = 30° the measure of ∠B is 60°
For ∠A = 45° the measure of ∠B is 45°
For ∠A = 60° the measure of ∠B is 30°
For ∠A = 75° the measure of ∠B is 15°
So, the sine and cosine of ∠A and ∠B would be,
∠A ∠B sin(A) cos(A) sin(B) cos(B)
15° 75° 0.25 0.97 0.97 0.26
30° 60° 0.5 0.87 0.87 0.5
45° 45° 0.71 0.71 0.71 0.71
60° 30° 0.87 0.5 0.5 0.87
75° 15° 0.97 0.26 0.26 0.97
From above records, we can observe that sin(A) = cos(B) and
sin(B) = cos(A)
Therefore, the relationship between the sine and cosine of ∠A and the sine and cosine of ∠B for given angles, sin(A) = cos(B) and
sin(B) = cos(A)
Learn more about complementary angles here:
https://brainly.com/question/5708372
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