cos((x-45))< 1/2 ,0<= x<= 360

Solution

cos ((x - 45)^{\circ}) < \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

No Solution for x \in R

Solution steps

cos ((x - 45)^{\circ}) < \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

Range of

cos ((x - 45)^{\circ}) :

False for all

y \in R

cos ((x - 45)^{\circ}) < \frac{1}{2} and

False for all

y \in R :

False

Let

y = cos ((x - 45)^{\circ})

Combine the intervals

y < \frac{1}{2} and False for all y \in R

Merge Overlapping Intervals

y < \frac{1}{2} and False for all y \in R

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

y < \frac{1}{2}

and

False for all

y \in R

False for all y \in R

False for all y \in R

Combine the intervals

False for all x \in R and 0^{\circ} \leq x \leq 36 0^{\circ}

No Solution for x \in R

cos (x) \leq \frac{2}{2}

cos (φ) \leq \frac{2}{2}

2 cos (y) > 0

cos (x) \leq - \frac{3}{2}, - π \leq x \leq π

0.96 (cos (x)) (sin (x)) \leq 0.43