Grade 11 math

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If the given point is on the terminal arm of an angle A in stadard position. 0 degrees more than or equal too A and less than or equal too 180 degree, find sin A and cos A:
a) (6,8) b) (-5,12)
Can you tell me how you get it because I do not understand it at all please help!

  • Grade 11 math -

    based on a right-angled triangle , you probably originally learned the following definitions of trig functions:
    sinØ = opposite/hypotenuse
    cosØ = adjacent/hypotenuse
    tanØ = opposite/adjacent

    by now I hope you also learned them in the following terms
    sinØ = y/r
    cosØ = x/r
    tanØ = y/x

    So after drawing your triangle for the terminal point (6,8)
    we know x=6, y=8 and r^2 = x^2 + y^2 = 100
    so r = 10
    so for the angle in the first quadrant
    sinØ = 8/10 = 4/5
    cosØ = 6/10 = 3/5
    tanØ = 8/6 = 4/3

    for the point (-5,12) the triangle is in the 2nd quadrant,
    x = -5, y = 12, and r = 13 , (r is considered always positive)
    sinØ = 12/13
    cosØ = -5/13
    tanØ = -12/5

    no matter what point you are given, plot the point and you will see which quadrant you are in.
    Draw the perpendicular to the x-axis (not the y-axis) and follow the steps I outlined.

  • Grade 11 math -

    I don'tquite understand we never learned y and r stuff. We just started this..the chapter is called Angles of rotation. Andwhere did u get the 10 from... and um sorry for bothering you but can u help me do one because there are many..:(
    Thanks I greatly appreciate you help!

  • Grade 11 math -

    plot (6,8)
    join to the origin (0,0)
    from (6,8) draw a perpendicular to the x-axis
    to get a right-angled triangle , with the line from the origin to the point (6,8) as the hypotenuse.
    If you are studying trig you must have learned the Pythagorean Theorem

    let the length of the hypotenuse be r
    then r^2 = 6^2 + 8^2
    r^2 = 36+64 = 100
    r = √100 = 10

    if you label the rotated angle Ø,
    then
    sinØ = opposite/hypotenuse = 8/10 = 4/5
    etc, see above

    notice for the point (6,8), the 6 is the x value, and the 8 is the y value.
    I hope that they will teach you very soon the trig definitions in terms of x, y , and r

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