1. ## Angles in Equation

If sin(2theta + 18) = cos(5theta - 12), which of the following pairs of angles are represented in this equation?

(a)42, 48 degrees
(b)38, 52 degrees
(c) 12, 68 degrees
(d) 45, 45 degrees

2. Hello, magentarita!

If $\sin(2\theta + 18) \:= \:\cos(5\theta - 12)$,

which of the following pairs of angles are represented in this equation?

. . $(a)\;42^o, 48^o \qquad (b)\;38^o, 52^o \qquad (c)\;12^o, 68^o \qquad (d)\; 45^o, 45^o$

If $\sin\alpha \,=\,\cos\beta$, then $\alpha\text{ and }\beta$ are complementary
. .
(of both angles are acute angles.)

So we have: . $(2\theta+18) +(5\theta - 12) \:=\:90^o\quad\Rightarrow\quad 7\theta \:=\:84^o \quad\Rightarrow\quad \theta \:=\:12^o$

The two angles are: . $\begin{array}{ccccc}2\theta + 18 &=&2(12) + 18 &=& 42^o \\ 5\theta-12 &=& 5(12) - 12 &=& 48^o \end{array}\quad\hdots$ answer (a)

3. Originally Posted by magentarita
If sin(2theta + 18) = cos(5theta - 12), which of the following pairs of angles are represented in this equation?

(a)42, 48 degrees
(b)38, 52 degrees
(c) 12, 68 degrees
(d) 45, 45 degrees

4. ## ok....

Originally Posted by Soroban
Hello, magentarita!

If $\sin\alpha \,=\,\cos\beta$, then $\alpha\text{ and }\beta$ are complementary
. . (of both angles are acute angles.)

So we have: . $(2\theta+18) +(5\theta - 12) \:=\:90^o\quad\Rightarrow\quad 7\theta \:=\:84^o \quad\Rightarrow\quad \theta \:=\:12^o$

The two angles are: . $\begin{array}{ccccc}2\theta + 18 &=&2(12) + 18 &=& 42^o \\ 5\theta-12 &=& 5(12) - 12 &=& 48^o \end{array}\quad\hdots$ answer (a)
I never would have found the answer alone. Thanks a lot.

5. ## ok...

Originally Posted by mr fantastic