What is the range of sin(x)+cos(x) ?

The range of sin(x)+cos(x) is -sqrt(2)<= f(x)<= sqrt(2)

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range of sin(x)+cos(x)

range

sin (x) + cos (x)

- 2 \leq f (x) \leq 2

Interval Notation

[- 2, 2]

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

sin (x) + cos (x) : - \infty < x < \infty

Extreme Points of

sin (x) + cos (x) :

Maximum

(\frac{π}{4} + 2 πn, 2),

Minimum

(\frac{5 π}{4} + 2 πn, - 2)

Find the range for the interval

- \infty < x < \infty : - 2 \leq f (x) \leq 2

Combine the ranges of all domain intervals to obtain the function range

- 2 \leq f (x) \leq 2

What is the range of sin(x)+cos(x) ?
The range of sin(x)+cos(x) is -sqrt(2)<= f(x)<= sqrt(2)