Question

Write the expression as either the sine, cosine, or tangent of a single angle.

sin(pi/2)cos(pi/7)+cos(pi/2)sin(pi/7)

Answer 1

@Hero

Answer 2

Use angle addition formulas

Answer 3

angle addition formulas?

Answer 4

@Hero which one?

Answer 5

http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities

Answer 6

so it'd be sin((pi/2)(pi/2))? I don't get it

Answer 7

So we want to apply the Sine Angle Addition formula:
\[\Large\rm \sin(\color{royalblue}{a})\cos(\color{orangered}{b})+\sin(\color{orangered}{b})\cos(\color{royalblue}{a})=\sin(\color{royalblue}{a}+\color{orangered}{b})\]
to our problem:\[\Large\rm \sin(\color{royalblue}{\pi/2})\cos(\color{orangered}{\pi/7})+\sin(\color{orangered}{\pi/7})\cos(\color{royalblue}{\pi/2})=?\]

Answer 8

sin((pi/2)+(pi/7))?

Answer 9

Mmm ok good!
Then just add them (get a common denominator).

Answer 10

sin(9pi/14)?

Answer 11

yay good job \c:/

Answer 12

Oh my gosh thank you sooooo much for this! :D