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Popular >

1+cos(2t)>= 0

Solution

1 + cos (2 t) \geq 0

Solution

True for all t \in R

+1

Interval Notation

(- \infty, \infty)

Solution steps

1 + cos (2 t) \geq 0

Move

1

to the right side

1 + cos (2 t) \geq 0

Subtract

1

from both sides

1 + cos (2 t) - 1 \geq 0 - 1

Simplify

cos (2 t) \geq - 1

cos (2 t) \geq - 1

Range of

cos (2 t) : - 1 \leq cos (2 t) \leq 1

Function range definition

The range of the basic

cos

function is

- 1 \leq cos (2 t) \leq 1

- 1 \leq cos (2 t) \leq 1

cos (2 t) \geq - 1 and - 1 \leq cos (2 t) \leq 1 : - 1 \leq cos (2 t) \leq 1

Let

y = cos (2 t)

Combine the intervals

y \geq - 1 and - 1 \leq y \leq 1

Merge Overlapping Intervals

y \geq - 1 and - 1 \leq y \leq 1

The intersection of two intervals is the set of numbers which are in both intervals

y \geq - 1

and

- 1 \leq y \leq 1

- 1 \leq y \leq 1

- 1 \leq y \leq 1

True for all t

True for all t \in R

Popular Examples

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15 cos (\frac{π}{15} x - \frac{2 π}{3}) + 95 \leq 105

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