Write the expression as the sine, cosine, or tangent of an angle.
sin(2π/9)cos(3π/8)+cos(2π/9)sin(3π/8)
Stella/Gray/Stacy -- please use the same name for your posts.
mmmmhhhh
I believe sin(A+B) = sinAcosB + cosAsinB
compare this to what you have
To write the expression sin(2π/9)cos(3π/8) + cos(2π/9)sin(3π/8) in terms of sine, cosine, or tangent of an angle, we can use the trigonometric identities for the sine and cosine of the sum of angles.
The identity we will use is:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
Let's assign the values of the angles in our expression:
a = 2π/9
b = 3π/8
Using the identity, we can rewrite the expression as:
sin(a)cos(b) + cos(a)sin(b) = sin(a + b)
So the expression sin(2π/9)cos(3π/8) + cos(2π/9)sin(3π/8) can be written as sin(2π/9 + 3π/8).
And there you have it! The expression can be expressed as the sine of an angle, which is sin(2π/9 + 3π/8).