Find the range of the function f ( x ) = 2 + sin

flightwingsd2

flightwingsd2

Answered question

2022-06-17

Find the range of the function f ( x ) = 2 + sin x 3 + cos x

Answer & Explanation

enfujahl

enfujahl

Beginner2022-06-18Added 20 answers

Write
y = 2 + sin x 3 + cos x
and rearrange as
sin x y cos x = 3 y 2
Use a compound angle transformation to rewrite the left hand side as
1 + y 2 sin ( x + α )
Knowing the range of sin enables us to write
| 3 y 2 1 + y 2 | 1
Squaring this and rearranging leads to
8 y 2 12 y + 3 0
So we end up with the range which is
1 4 ( 3 3 ) y 1 4 ( 3 + 3 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?