Write the Word or Phrase That Best Completes Each Statement $$\mathrm { R } = \frac { \mathrm { v } \mathrm { v } _ { 0 } ^ { 2 } } { \mathrm {~g} } \sin ( 2 \theta$$

Write the word or phrase that best completes each statement or answers the question.
-The path of a projectile fired at an inclination θ (in degrees) to the horizontal with an initial speed v0 is a
parabola. The range R of the projectile, that is, the horizontal distance that the projectile travels, is found by using the
formula $$\mathrm { R } = \frac { \mathrm { v } \mathrm { v } _ { 0 } ^ { 2 } } { \mathrm {~g} } \sin ( 2 \theta$$ where g is the acceleration due to gravity. The maximum height H of the projectile is $$\mathrm { H } = \frac { \mathrm { v } _ { 0 } ^ { 2 } } { 4 \mathrm {~g} } ( 1 - \cos ( 2 \theta ) )$$ Find the range R and the maximum height H in terms of g if the projectile is fired with an initial speed of 200 meters per
second at an angle of 15° and then at an angle of 22.5°. Do not use a calculator, but simplify the answers.