Question

solve the following equation for the value of theta between 0 degrees and 360 degrees.For 5 + 3cosec^2theta =8

Answer 1

5 + 3 cosec ^ 2 (theta) = 8

3 cosec ^ 2 (theta) = 8 - 5

3 cosec ^ 2 (theta) = 3 Divide both sides by 3

cosec ^ 2 (theta) = 3 / 3

cosec ^ 2 (theta) = 1

cosec (theta) = sqrt ( 1 )

cosec (theta) = + OR - 1


cosec ( theta ) = 1 / sin ( theta )

sin ( theta ) = 1 / cosec ( theta )

sin ( theta ) = + OR - 1



cosec 90 ° = 1

cosec 270 ° = - 1

OR

sin 90 ° = 1

sin 270 ° = - 1


Solutions :


theta = 90 °

and

theta = 270 °