What is the range of sin(t)-(cos(t)+sin(t)) ?

The range of sin(t)-(cos(t)+sin(t)) is -1<= f(t)<= 1

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range of sin(t)-(cos(t)+sin(t))

range

sin (t) - (cos (t) + sin (t))

- 1 \leq f (t) \leq 1

Interval Notation

[- 1, 1]

Solution steps

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

Domain of

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

Simplify

sin (t) - (cos (t) + sin (t)) : - cos (t)

Extreme Points of

- cos (t) :

Minimum

(2 πn, - 1),

Maximum

(π + 2 πn, 1)

Find the range for the interval

- \infty < t < \infty : - 1 \leq f (t) \leq 1

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

- 1 \leq f (t) \leq 1

3 cos (4 x)

f (x) = (2 x - 14)^{4}

f (x) = (x - 2)^{3} + 3

- (x - 1)^{2} + 4

f (x) = 2 x 4 - x^{2}

What is the range of sin(t)-(cos(t)+sin(t)) ?
The range of sin(t)-(cos(t)+sin(t)) is -1<= f(t)<= 1