To find cos(8) given that sin(8) = 21/29, we can use the Pythagorean identity which states:
sin²(θ) + cos²(θ) = 1
In our case, θ is 8 degrees. First, we calculate sin²(8):
sin²(8) = (21/29)² = 441/841
Now we can substitute sin²(8) into the Pythagorean identity:
441/841 + cos²(8) = 1
To isolate cos²(8), we subtract sin²(8) from both sides:
cos²(8) = 1 – 441/841
To perform the subtraction, we can convert 1 into a fraction with a denominator of 841:
1 = 841/841
Now we have:
cos²(8) = 841/841 – 441/841 = 400/841
Next, we take the square root to find cos(8):
cos(8) = ±√(400/841) = ±20/29
Since cosine is positive in the first quadrant (and angles like 8 degrees would typically be in the first quadrant), we take the positive root:
cos(8) = 20/29