For the following exercises, find all solutions exactly on the interval 0≤θ<2π. 1. 2 sin θ =3–√

2. 2 cos θ =−2–√

3. tan x= 1

4. 4 sin 2x −2 =0

The rows and columns of lattice points in a three-by-three square array are evenly spaced one unit apart. how many distinct triangles with at least one side of length 2 units can be drawn using three lattice points for the vertices?

Consider the following equation -167 + 37 = 49 - 21p select the equation that has the same solution as the given equation. o a. p - 5 + ip = 7 - p ob. +55 + 12p = 5p + 16 c. 2 + 1.25p = -3.75p + 10 d. -14 + 6p = -9 - 6p reset next

Abilliard ball is struck by a cue. it travels 1 0 0 cm 100cm before ricocheting off a rail and traveling another 1 2 0 cm 120cm into a corner pocket. the angle between the path as the ball approaches the rail and the path after it strikes the rail is 4 5 ∘ 45 ∘ . how far is the corner pocket from where the cue initially struck the ball? do not round during your calculations. round your final answer to the nearest centimeter.