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Math Help - Angles in Equation

  1. #1
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    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

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  2. #2
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    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)

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  3. #3
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    Quote Originally Posted by magentarita View Post
    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
    See also the comments in post #3 of http://www.mathhelpforum.com/math-he...2-solve-x.html
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  4. #4
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    ok....

    Quote Originally Posted by Soroban View Post
    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.
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  5. #5
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    ok...

    Quote Originally Posted by mr fantastic View Post
    See also the comments in post #3 of http://www.mathhelpforum.com/math-he...2-solve-x.html
    Thanks for the link.
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