Final answer:
To write a trigonometric expression as a constant, we use trigonometric identities to eliminate variables and functions. For example, we can rewrite sin(x) + cos(x) as 2cos(45)cos(0) ≈ √2/2
Step-by-step explanation:
To write a trigonometric expression as a constant, we need to eliminate any variables or functions. One way to do this is by using special trigonometric identities. For example, if we have the expression sin(x) + cos(x), we can rewrite it using the identity sin(x) = cos(90 - x): cos(90 - x) + cos(x).
Now, we can combine the cosines using the identity cos(A) + cos(B) = 2cos((A+B)/2)cos((A-B)/2): 2cos((90 - x + x)/2)cos((90 - x - x)/2).
Simplifying further, we get 2cos(90/2)cos(0/2), which is equal to 2cos(45)cos(0).
Finally, we can express this as a constant by approximating cos(45) to √2/2: