Question

Use an appropriate Half-Angle Formula to find the exact value of the expression.
sin(7π/8)????

Answer 1

\(\Huge\color{blue}{ \tt π=180° }\)

\(\Huge\color{blue}{ \tt 7π/8=7(180)/8=?}\)

Answer 2

you tell me

Answer 3

i forgot the formula for half angle for sin

Answer 4

\[\sin(\theta/2)= \pm \frac {\sqrt{1-\cos(\theta)}} {2}\] \]

Answer 5

\[\sin(\theta/2)= \pm \frac {\sqrt{1-\cos(\theta)}} {2}\]

Answer 6

you angle is 157.5 so...

\(\Huge\color{blue}{ \sf sin \frac{315}{2} = ±\frac{ \sqrt{1-cos(315)} }{2} }\)

for cos315, use

cos(315)=cos(360-45)

Answer 7

cos(A-B)=cos A cos B + sin A sin B

Answer 8

and the 315 came from where ?

Answer 9

because you are using half angle formula, and 157.5=315/2

Answer 10

cos(A-B)=cos A cos B + sin A sin B
cos(315) = cos(360-45) = cos 360 cos 45 + sin 360 sin 45 = 1 * (sqrt 2)/2 + 0 * (sqrt 2)/2 = (sqrt 2)/2

Answer 11

\[1-\sqrt{2}/2\]/2

Answer 12

\(\Huge\color{blue}{ \sf Sin\frac{315}{2}= \frac{\sqrt{1- \frac{ \sqrt{2} }{2} } }{2} }\)


\(\Huge\color{blue}{ \sf Sin\frac{315}{2}= \frac{\sqrt{\frac{2}{2}- \frac{ \sqrt{2} }{2} } }{2} }\)

\(\Huge\color{blue}{ \sf Sin\frac{315}{2}= \frac{\sqrt{ \frac{ 2-\sqrt{2} }{2} } }{2} }\)



hold....