Results 1 to 5 of 5

Math Help - [SOLVED] Trig definitions and identities

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    175

    [SOLVED] Trig definitions and identities

    I have my book open here with the definitions and fundamental identities to sine cosine and tangent.

    For example, sine theta is y/r and 1/csc theta

    It does not list csc, sec and cot. How can I find these?

    What if we have arcsin (inverse of sin), what would the csc be?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by thekrown View Post
    I have my book open here with the definitions and fundamental identities to sine cosine and tangent.

    For example, sine theta is y/r and 1/csc theta

    It does not list csc, sec and cot. How can I find these?

    What if we have arcsin (inverse of sin), what would the csc be?
    Whilde defining sin(theta), where did you get y and r from? Are you using a right angled triangle with an angle theta to determine the trigonometric identities? Please state clearly.

    similarly, csc(theta) = 1/sin(theta)
    sec(theta)= 1/cos(theta)
    cot(theta) = 1/tan(theta)

    arc sin is the same as csc!
    arcsin(theta)= (inverse of sin(theta)) = 1/sin(theta) = csc(theta)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    Posts
    175
    Most of our triangles are 45 or 30/60's. The y/r comes from a different of viewing the adjacent/opposite business which I find overlycomplicated...

    I use y/r because I simplify the 45 and 30/60 triangles to radius 1 and always end up with the same values.

    This might be why I'm having trouble with calculus trig.

    The teachers didn't tell us this, so I must somehow know this but I don't. Thank you for your help.

    Is it safe to say that csc, sec, cot are inverses of sin, cos, tangent and vice versa?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by thekrown View Post
    I have my book open here with the definitions and fundamental identities to sine cosine and tangent.

    For example, sine theta is y/r and 1/csc theta

    It does not list csc, sec and cot. How can I find these?

    What if we have arcsin (inverse of sin), what would the csc be?
    Hi thekrown,

    Visualize a circle with center (0, 0) and radius = r. Pick a point on the circle in quadrant 1, for example, and call it P(x, y).

    Draw a perpendicular to the x-axis from this point. The degree of rotation is the measure of the angle formed by the radius and the x-axis. Let's call this angle \theta.

    The side opposite this angle is y units long.
    The side adjacent to this angle is x units long.
    The radius is r units long.

    The six trigonometric functions of this angle are defined this way.

    \sin \theta=\frac{y}{r} <====> \csc \theta=\frac{r}{y}

    \cos\theta=\frac{x}{r} <====> \sec \theta=\frac{r}{x}

    \tan\theta=\frac{y}{x} <====> \cot \theta=\frac{x}{y}

    To understand arcsin, sometimes written \sin^{-1},
    recall just as y=\sqrt{x} is defined such that y^2=x,
    y=\arcsin x is defined so that \sin y = x






    Quote Originally Posted by harish21 View Post
    Whilde defining sin(theta), where did you get y and r from? Are you using a right angled triangle with an angle theta to determine the trigonometric identities? Please state clearly.

    similarly, csc(theta) = 1/sin(theta)
    sec(theta)= 1/cos(theta)
    cot(theta) = 1/tan(theta)

    arc sin is the same as csc!
    arcsin(theta)= (inverse of sin(theta)) = 1/sin(theta) = csc(theta)
    Arcsin is not the reciprocal of sine. It's the inverse of sine. The reciprocal of sine (sin) is cosecant (csc).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by harish21 View Post
    Whilde defining sin(theta), where did you get y and r from? Are you using a right angled triangle with an angle theta to determine the trigonometric identities? Please state clearly.

    similarly, csc(theta) = 1/sin(theta)
    sec(theta)= 1/cos(theta)
    cot(theta) = 1/tan(theta)

    arc sin is the same as csc! no!!
    arcsin(theta)= (inverse of sin(theta)) = 1/sin(theta) = csc(theta) no! it's not
    arcsin(x)=sin^{-1}(x)

    returns an angle

    \frac{1}{sin(x)}=csc(x)

    The "inverse function" is not the same as the "inverse" of the function,
    if the terms are rigorously adhered to.

    Edit:
    Sorry masters!!
    I didn't see you spotted it
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] trig identities
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: November 17th 2009, 04:03 PM
  2. [SOLVED] Proving trig identities
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: April 28th 2009, 01:42 PM
  3. [SOLVED] Verifying Trig identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 5th 2009, 05:16 PM
  4. [SOLVED] Trig Identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 1st 2009, 09:29 AM
  5. [SOLVED] Trig identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 26th 2008, 12:14 PM

Search Tags


/mathhelpforum @mathhelpforum