Final answer:
Given the sine of angle 'a', we found the cosine of 'a' using the Pythagorean identity, arriving at an exact value of cos(a) = 12/13 for the function value.
Step-by-step explanation:
Given that sin(a) = 5/13, and assuming 'a' is in the first quadrant (since trigonometric functions are positive there and we are given a positive sine value), we can find the cosine of angle 'a' using the Pythagorean identity sin^2(a) + cos^2(a) = 1. Here's how you can calculate this:
- Firstly, square the sine value: (5/13)^2 which equals 25/169.
- Secondly, subtract that value from 1 to get cos^2(a): 1 - (25/169) = (169/169) - (25/169) = 144/169.
- Then, take the positive square root of that result, since we are assuming 'a' is in the first quadrant: cos(a) = √(144/169) = 12/13.
You have found the exact cosine value for angle 'a', which is 12/13.
If the question is asking for another trigonometric function value (such as finding sin(π/2 + a)), you'll need to apply relevant trigonometric identities using the found sine and cosine values. However, without further information, we'll focus on finding the cosine value as the exact function value for this response.
Remember to check if your final answer makes sense and is consistent with the trigonometric function properties.