Solve the equation for t.

Question

The equation models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released. Solve the equation for t.  (pi as in 3.14)

 

h = 7cos (pi/3 t)

Answer 1

h = 7 cos (pi/3 * t)

 

h/7 = cos (pi/3 * t)

 

(pi/3 * t) = cos^-1(h/7)

 

t = (3/pi) * cos^-1(h/7)

 

Now keep in mind that the inverse cosine is multivalued, so there will be infinitely many t's coming out of this, because of the periodicity of the cosine.