Question

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

Answer 1

You will need to use the identity

\[\Large \sin(x+y) = \sin(x)\cos(y)+\cos(x)\sin(y)\]

Answer 2

can you walk me through this? Which values stand for x and y

Answer 3

x = pi/2

y = pi/7

Answer 4

yes you'll plug in x = pi/2 & y = pi/7

Answer 5

so...
\[\sin(\pi/2+\pi/7)= \sin(\pi/2)\cos(\pi/7) + \cos(\pi/2)\sin(\pi/7)\]

Answer 6

yes

Answer 7

where do i go from here?

Answer 8

now combine pi/2+pi/7

Answer 9

get each denominator equal to the LCD

Answer 10

\[\sin(7\pi/14+2\pi/14)=\sin(7\pi/14)\cos(2\pi/14)\cos(7\pi/14)\sin(2\pi/14)\]

Answer 11

no need to alter the right side

Answer 12

just the left side (the pi/2 + pi/7)

Answer 13

but now you can add 7pi/14 + 2pi/14

Answer 14

alright so now we got sin 9pi/14= {the rest of the equation}

Answer 15

yep,
\[\Large \sin\left(\frac{\pi}{2}\right)\cos\left(\frac{\pi}{7}\right)+\cos\left(\frac{\pi}{2}\right)\sin\left(\frac{\pi}{7}\right) = \sin\left(\frac{9\pi}{14}\right)\]

Answer 16

so \[\sin(9\pi/14)\] is my answer?

Answer 17

yes it is