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Math Help - Angles

  1. #1
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    Angles

    Good day,hope I'm welcome

    I'm having problem solving these

    Find the circular functions of the following:

    a. 36 deg
    b. 22 deg and 30 minutes
    c. 15 deg = ( 30 deg / 2 )

    For a. I tried to find special angles(30,60,45,and other quadrantal angles) that would sum up to 36 deg , but I just can't find any.

    Same goes for letter b.

    And for letter c. I can't think of any procedure that will direct me to the correct answer, using 30 deg / 2.

    Hoping for replies.

    Thanks
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  2. #2
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    Quote Originally Posted by ImKo View Post
    Good day,hope I'm welcome

    I'm having problem solving these

    Find the circular functions of the following:

    a. 36 deg
    b. 22 deg and 30 minutes
    c. 15 deg = ( 30 deg / 2 )

    For a. I tried to find special angles(30,60,45,and other quadrantal angles) that would sum up to 36 deg , but I just can't find any.

    Same goes for letter b.

    And for letter c. I can't think of any procedure that will direct me to the correct answer, using 30 deg / 2.

    ...
    I'm confused about what you are asked to calculate ... But maybe this helps a little bit further:

    All the given values of the angles are integer parts of 360:

    36^\circ = \dfrac1{10} \cdot 360^\circ


    22^\circ 30' = \dfrac12 \cdot 45^\circ = \dfrac1{16} \cdot 360^\circ


    15^\circ = \dfrac1{24} \cdot 360^\circ
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  3. #3
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    Quote Originally Posted by ImKo View Post
    Good day,hope I'm welcome

    I'm having problem solving these

    Find the circular functions of the following:

    a. 36 deg
    b. 22 deg and 30 minutes
    c. 15 deg = ( 30 deg / 2 )

    For a. I tried to find special angles(30,60,45,and other quadrantal angles) that would sum up to 36 deg , but I just can't find any.

    Same goes for letter b.

    And for letter c. I can't think of any procedure that will direct me to the correct answer, using 30 deg / 2.

    Hoping for replies.

    Thanks
    Are you asking for their radian measure?

    Remember that a "radian" is the length of a radius on the circumference of a circle. Since it is the length of the radius on the CIRCUMFERENCE, it is given the symbol C.

    If the circle has unit radius (i.e. radius = 1), then

    C = 2\pi r = 2\pi\times 1 = 2\pi^C.

    So there are 2\pi radians in a circle.

    Recall that there are also 360^{\circ} in a circle.

    So 360^{\circ} = 2\pi^C

    So 1^{\circ} = \frac{\pi}{180}^C.


    So to find the number of radians in a certain number of degrees, multiply by

    \frac{\pi}{180}.
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  4. #4
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    We are asked to find the

    sine, cosine, tangent, cosecant, secant, cotangent of the following angles

    like sin30 deg = 1/2.......etc

    It would be best if it is in radical form

    Hope it clears things.

    Thanks for any help
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  5. #5
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    Quote Originally Posted by ImKo View Post
    We are asked to find the

    sine, cosine, tangent, cosecant, secant, cotangent of the following angles

    like sin30 deg = 1/2.......etc

    It would be best if it is in radical form

    Hope it clears things.

    Thanks for any help
    OK, in that case, for b) and c) you need to use the half angle formulas...

    \sin{\frac{\theta}{2}} = \pm \sqrt{\frac{1 - \cos{\theta}}{2}}

    \cos{\frac{\theta}{2}} = \pm \sqrt{\frac{1 + \cos{\theta}}{2}}

    \tan{\frac{\theta}{2}} = \frac{\sin{\theta}}{1 + \cos{\theta}}.
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  6. #6
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    Thanks I got the sin, cos, and the tan, already

    So..........How do I get the sec, csc, cot ?

    Should I get their reciprocals?

    and when should I use these formulas?

    tan y/2 = 1- cos y / sin y

    tan y/2 = sin y / 1 + cos y

    Thanks
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  7. #7
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    Quote Originally Posted by ImKo View Post
    Thanks I got the sin, cos, and the tan, already

    So..........How do I get the sec, csc, cot ?

    Should I get their reciprocals?

    and when should I use these formulas?

    tan y/2 = 1- cos y / sin y

    tan y/2 = sin y / 1 + cos y

    Thanks
    Yes, once you've got sin, cos and tan, just take their reciprocals and you have the csc, sec and cot.

    As for the tan formulae, you wanted to find \tan{22^{\circ}30'} = \tan{\frac{45^{\circ}}{2}} and \tan{15^{\circ}} = \tan{\frac{30^{\circ}}{2}} didn't you?
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  8. #8
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    Never mind my other question. I had an error there

    My question was supposed to be


    "when should I use these identities

    tan^2 y /2 = 1 - cos y / 1 + cos y
    tan y /2 = 1 - cos y / sin y
    tan y /2 = sin y / 1 + cos y

    since they are all Tangent-Half-Measure Identities" I was thinking they are all of different uses

    Later on I found out they are all just equal, After some computations

    As for letter a. how should I solve it?

    Anyway thanks for the help!

    And HAPPY NEW YEAR TO ALL, its December 31, 2008 here waiting for the New Year to come 1 hour or so from now its already 2009!!
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