use the half - angle formulas to find the exact value of the expression ( sinleft(-\frac{3pi}{8}\right)…

use the half - angle formulas to find the exact value of the expression ( sinleft(-\frac{3pi}{8}\right) ).\nwhich half - angle formula should be used to find the exact value of the ( sinleft(-\frac{3pi}{8}\right) )? select the correct choice below and fill in the answer boxes to complete your choice.\n(type an exact answer in terms of ( pi ).)\na. ( sinleft(-\frac{3pi}{8}\right)=-sinleft(\frac{square}{2}\right)=-sqrt{\frac{1 - cossquare}{2}} )\nb. ( sinleft(-\frac{3pi}{8}\right)=-sinleft(\frac{square}{2}\right)=-sqrt{\frac{1 - cossquare}{2}} )\nc. ( sinleft(-\frac{3pi}{8}\right)=sinleft(\frac{square}{2}\right)=sqrt{\frac{1 + cossquare}{2}} )\nd. ( sinleft(-\frac{3pi}{8}\right)=sinleft(\frac{square}{2}\right)=sqrt{\frac{1 + cossquare}{2}} )\n( sinleft(-\frac{3pi}{8}\right)=square )\n(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

use the half - angle formulas to find the exact value of the expression ( sinleft(-\frac{3pi}{8}\right) ).\nwhich half - angle formula should be used to find the exact value of the ( sinleft(-\frac{3pi}{8}\right) )? select the correct choice below and fill in the answer boxes to complete your choice.\n(type an exact answer in terms of ( pi ).)\na. ( sinleft(-\frac{3pi}{8}\right)=-sinleft(\frac{square}{2}\right)=-sqrt{\frac{1 - cossquare}{2}} )\nb. ( sinleft(-\frac{3pi}{8}\right)=-sinleft(\frac{square}{2}\right)=-sqrt{\frac{1 - cossquare}{2}} )\nc. ( sinleft(-\frac{3pi}{8}\right)=sinleft(\frac{square}{2}\right)=sqrt{\frac{1 + cossquare}{2}} )\nd. ( sinleft(-\frac{3pi}{8}\right)=sinleft(\frac{square}{2}\right)=sqrt{\frac{1 + cossquare}{2}} )\n( sinleft(-\frac{3pi}{8}\right)=square )\n(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Analyze the sign of the sine function

The angle (-\frac{3\pi}{8}) is in the fourth - quadrant. In the fourth - quadrant, the sine function is negative, so (\sin\left(-\frac{3\pi}{8}\right)=-\sin\left(\frac{3\pi}{8}\right)).

Step2: Apply the half - angle formula

The half - angle formula for sine is (\sin\frac{\alpha}{2}=\pm\sqrt{\frac{1 - \cos\alpha}{2}}). Let (\frac{\alpha}{2}=\frac{3\pi}{8}), then (\alpha=\frac{3\pi}{4}).

Answer:

B. (\sin\left(-\frac{3\pi}{8}\right)=-\sin\left(\frac{3\pi}{8}\right)=-\sqrt{\frac{1-\cos\frac{3\pi}{4}}{2}})