Solving Trig Equations

This week we learned to solve trig equations.  To do this, you solve the equation as though you have a regular equation.  Then you find the angle that has that value.  Then you determine what quadrants the angles are.  Finally, you convert the two degree values to degrees, minutes, and seconds.

Solve 4sinѲ=3 for 0˚ ≤ Ѳ ≤ 360˚.  Give answers in degrees, minutes, and seconds.

4sinѲ=3

      (4sinѲ)/4=3/4    divide both sides by 4

     sinѲ= .75

     Ѳ=sin^-1 (.75)= 48.5903

     Sin is positive in quadrant I and II.  So the second angle in quadrant II is 180 - 48.5903 =  131.4097

     Finally, change each angle to degrees, minutes and seconds.

1)      Ѳ=48.5903

48.5903 – 48 = .5903 x 60 = 35.418

35.418 – 35 = .418 x 60 = 25.08

Ѳ = 48˚35’25”

 Ѳ=131.4097

131.4097 – 131 = .4097 x 60 = 24.582

24.582 – 24 = .582 x 60 = 34.92

Ѳ = 131˚24’35”

Jenna Roussel