8 What is the exact value of the trigonometric expression in

8.

What is the exact value of the trigonometric expression in simplest form?

sin(5/6)+2tan(7/4)

1/2+2

1/22

3/2

3/2

Solution

given sin(5/6)+2 tan(7/4)

tan(7/4) ==> tan ( (3 + 4) / 4 ) ===> tan ( (3/4 + 4/4) )

===> tan ( (3/4 + 1) ) ==> tan ( + 3/4 )

since use the periodicity of tan tan ( x + * k ) ==> tan ( x )

===> tan ( + 3/4 ) ==> tan (3/4 )

==> sin(5/6)+ 2   tan (3/4 )

===> sin ( /2 + /3 ) + 2 tan ( /2 + /4 )

==> cos ( /3 ) + 2 * -co t( /4 ) ( in II quadrant sin , cos are only positives )

==> 1/2 - 2 * 1

===> 1/2 -2 ==> - 3/2