[Triangle] Find sin 1),sin #,cos 1), and cos &. Write each answer as a fraction in simplest form.

If ${\displaystyle \sin x+\sin y=a\text{and}\cos x+\cos y=b}$ then find ${\displaystyle \tan (x-\frac{y}{2})}$

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute.

Use function notation to describe the way the second variable (DV) depends upon the first variable (IV). Determine the domain and range for each, determine if there is a positive, negative, or no relationship, and explain your answers.
A)IV: an acute angle V in a right triangle: DV: the area B of the triangle if the hypotenuse is a fixed length G.
B)IV: one leg P of a right triangle: DV: the hypotenuse G of the right triangle if the other leg is 2
C)IV: the hypotenuse G of a right triangle: DV: the other leg P of the right triangle is one leg is 5.

For Exercises 56-58, use ${\displaystyle {\log }_{b}2\approx 0.289,{\log }_{b}3\approx 0.458,\text{ and }{\log }_{b}5\approx 0.671\text{ to approximate the value of the given logarithms.}}$
${\displaystyle 56.{\log }_{b}8}$
${\displaystyle 57.{\log }_{b}45}$
${\displaystyle 58.{\log }_b\left(\frac{1}{9}\right)}$

When solving a trigonometric equation, the preliminary goal is to ? the trigonometric function on one side of the equation.

${\displaystyle \sec 2x-1=0[0,2\pi )}$
solve for x

If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides ____________________.