Use the halfangle formulas to determine the exact values of

Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle. 75°

Sin(75deg)=

Cos(75deg)=

Tan(75deg)=

Solution

cos(150) = cos ( 180-30) = - cos 30 = - 0.866

i) from cos@ = 1- 2*sin²( @/2)

sin ( @/2) = ( 1- cos @/ 2)^1/2

ie sin(75) = ( 1- cos 150 / 2)^1/2

= ( 1- ( - 0.866) / 2)^1/2

= 0.9559

ii) from cos @ = 2*cos² ( @/2) - 1

cos(@/2) = ( cos@ + 1 / 2)^1/2

ie cos(75) = ( cos 150 +1 / 2)^1/2

= 0.2588

iii) tan(75) = sin(75) / cos(75)

= 3.693