59.8k views
0 votes
Evaluate each expression given that.

f(x) = sin x g(x) = cos x
h(x) = tan x k(x) = 2x

Exact values or expressions are required, not calculator approximations.
(a) f (/6+5/6)
(b) f (5/6) + f(13/6)

User Yili
by
8.3k points

1 Answer

5 votes

Final answer:

For (a), assuming a typo and that the expression should be π/6 + 5/6, f(π/6 + 5/6) equals sin(π), which is 0. For (b), f(5/6) + f(13/6) simplifies to 2sin(5/6) because 13/6 is equivalent to 2π + 1/6 and sine function has a period of 2π.

Step-by-step explanation:

To evaluate the expressions using the functions provided, we can use identities from trigonometry. We have f(x) = sin x, g(x) = cos x, h(x) = tan x, and k(x) = 2x. For the given expressions, we must remember that the arguments for trigonometric functions are in radians.

(a) For f(\(ð + 5/6)), it seems there might be a typo, as \(ð is not a standard notation or number. Assuming it should be π/6, then f(π/6 + 5/6) = sin(π) because π/6 + 5/6 = 1π (or 6π/6), and we know sin(π) = 0.

(b) The second expression can be evaluated directly: f(5/6) + f(13/6). Since 13/6 is the same as 2π + 1/6 (because 2π is one full rotation in radians), f(5/6) = sin(5/6), and f(13/6) = sin(5/6) because sin has a period of 2π. Therefore, f(5/6) + f(13/6) = sin(5/6) + sin(5/6) = 2sin(5/6).

User Eusid
by
9.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories