Question

Use the Half Angle Formulas to find the exact value of the following. You may have need of the Quotient, Reciprocal or Even/Odd Identities as well.

sin (3π/8)

Answer 1

`\bf 2\cdot \cfrac{3}{8}\implies \cfrac{3}{4}\qquad thus \\\\\\ sin\left( \cfrac{3\pi }{8} \right)\iff sin\left( \cfrac{(3\pi )/(4)}{2} \right)=\pm \sqrt{\cfrac{1-cos\left( (3\pi )/(4) \right)}{2}} \\\\\\ sin\left( \cfrac{(3\pi )/(4)}{2} \right)=\pm \sqrt{\cfrac{1-\left( -(√(2))/(2) \right)}{2}}\implies sin\left( \cfrac{(3\pi )/(4)}{2} \right)=\pm \sqrt{\cfrac{(2+√(2))/(2)}{2}} \\\\\\ sin\left( \cfrac{(3\pi )/(4)}{2} \right)=\pm\sqrt{\cfrac{2+√(2)}{4}}`