# Compound Angle Formula

• May 11th 2010, 07:07 AM
coolhacker
Compound Angle Formula
Hi everyone!

plz help me solve this Compound Angle Formula question:

1. Using Compound Angle Formula, prove that:

cos(y - 180°) + sin (y +
90°) = 0

plz thxx
(Clapping)(Talking)
• May 11th 2010, 07:32 AM
harish21
Quote:

Originally Posted by coolhacker
Hi everyone!

plz help me solve this Compound Angle Formula question:

1. Using Compound Angle Formula, prove that:

cos(y - 180°) + sin (y +
90°) = 0

plz thxx
(Clapping)(Talking)

$\displaystyle cos(A-B) = (cosA \times cosB) + (sinA \times sinB)$

$\displaystyle sin(A+B) = (sinA \times cosB) + (cosA \times sinB)$

• May 11th 2010, 07:37 AM
Soroban
Hello, coolhacker!

We are expected to know these formulas:

. . $\displaystyle \cos(A-b) \;=\;\cos A\cos B + \sin A\sin B$

. . $\displaystyle \sin(A + B) \;=\;\sin A\cos B + \cos A\sin B$

Quote:

1. Using Compound Angle Formulas, prove that:

. . . . . $\displaystyle \cos(y - 180^o) + \sin (y + 90^o) \;=\;0$

We have: . $\displaystyle \cos(y-180^o) \qquad\quad+ \quad\qquad\sin(y+90^o)$

. . $\displaystyle =\;\;\overbrace{\cos y \cos180^o + \sin y \sin180^o} + \overbrace{\sin y\cos90^o + \cos y\sin90^o}$

. . $\displaystyle =\;\;\;\cos y\,(-1) \quad+\quad \sin y\,(0) \quad+\quad \sin y\,(0) \quad+ \quad \cos y\,(1)$

. . $\displaystyle =\qquad -\cos y \qquad + \qquad 0 \qquad + \qquad 0 \qquad + \qquad \cos y$

. . $\displaystyle =$ . . . . . . . . . . . . . . . . . .$\displaystyle 0$

• May 11th 2010, 07:56 AM
coolhacker
thx u