Answer: the value of cos(a-B) is 0.7065.
Step-by-step explanation:
To find the value of cos(a-B), we can use the cosine difference formula, which states:
cos(a-B) = cos(a)cos(B) + sin(a)sin(B)
Given that cos(a) = 0.973, sin(a) = √(1 - cos^2(a)) = √(1 - 0.973^2), and sin(B) = 0.687, we can calculate sin(a) as follows:
sin(a) = √(1 - cos^2(a))
sin(a) = √(1 - 0.973^2)
sin(a) = √(1 - 0.946729)
sin(a) ≈ √0.053271
sin(a) ≈ 0.2307
Now, we can substitute these values into the cosine difference formula:
cos(a-B) = cos(a)cos(B) + sin(a)sin(B)
cos(a-B) = 0.973 * cos(B) + 0.2307 * 0.687
cos(a-B) = 0.973 * cos(B) + 0.158477
To find the value of cos(B), we can use the Pythagorean identity sin^2(B) + cos^2(B) = 1, since sin(B) = 0.687:
sin^2(B) + cos^2(B) = 1
0.687^2 + cos^2(B) = 1
0.472369 + cos^2(B) = 1
cos^2(B) = 1 - 0.472369
cos^2(B) = 0.527631
cos(B) ≈ √0.527631
cos(B) ≈ 0.7261
Now, substitute cos(B) back into the previous equation:
cos(a-B) = 0.973 * 0.7261 + 0.158477
cos(a-B) ≈ 0.7065
Therefore, the value of cos(a-B) would be 0.7065.
