so the question im having trouble with is..
Use the appropriate compound angle formula to determine the exact value of each expression.
a) sin (π+π/6)
i keep on getting -√3/2 when ever i do it but the answers in the back of the textbook says it equals -1/2 and i have no clue what im doing ...
Use the appropriate compound angle formula to determine the exact value of each expression.
a) sin (π+π/6)
i keep on getting -√3/2 when ever i do it but the answers in the back of the textbook says it equals -1/2 and i have no clue what im doing ...
-
Okay, so you are using the sin(x+y)=sinxcosy + cosxsiny equation here. So start by subbing the values into the equation.
You get sin(π+π/6)=sin(π)cos(π/6)+(cosπ)(sinπ/6)…
= (0)(√3/2)+(-1)(1/2)
= -1/2
When you simplify 0 and √3/2 that is 0 and -1x1/2 is the same as -1/1 x 1/2 which is -1/2. Hope I helped!
You get sin(π+π/6)=sin(π)cos(π/6)+(cosπ)(sinπ/6)…
= (0)(√3/2)+(-1)(1/2)
= -1/2
When you simplify 0 and √3/2 that is 0 and -1x1/2 is the same as -1/1 x 1/2 which is -1/2. Hope I helped!
-
sin (u + v) = sin u cos v + cos u sin v
sin (pi + pi/6) = sin pi cos pi/6 + cos pi sin pi/6
sin pi = 0
cos pi/6 = sqrt(3) / 2
cos pi = -1
sin pi/6 = 1/2
sub to give: sin (pi + pi/6) = (0)(sqrt(3) / 2) + (-1)(1/2) = -1/2
sin (pi + pi/6) = -1/2
by the way, pi + pi/6 = 7pi/6, and you should recognize that sin (7pi/6) = -1/2
sin (pi + pi/6) = sin pi cos pi/6 + cos pi sin pi/6
sin pi = 0
cos pi/6 = sqrt(3) / 2
cos pi = -1
sin pi/6 = 1/2
sub to give: sin (pi + pi/6) = (0)(sqrt(3) / 2) + (-1)(1/2) = -1/2
sin (pi + pi/6) = -1/2
by the way, pi + pi/6 = 7pi/6, and you should recognize that sin (7pi/6) = -1/2