Give an example, with justification:
A real life situation requiring the use of a trigonometry identity.
Knowledge is life, so open your doors of perception.
Here is one use of identities that is introduced to students in a high school physics class ... the derivation of the range formula for the horizontal displacement of a projectile (Galilean model).
start with the physics equation for vertical displacement ...
since the projectile lands at the same height it started,
...
solving for t ...
horizontal displacement is given by the formula ...
using the last two equations, eliminate the parameter t ...
using the double angle identity
,
the last equation becomes ...
from this equation, it can be deduced that the launch angle for maximum horizontal range is 45 degrees.