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Math

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1) evaluate without a calculator: a)sin(3.14/4) b) cos(-3(3.14)/4) c) tan(4(3.14)/3) d) arccos(- square root of three/2) e) csctheata=2
2) verify the following identities: a) cotxcosx+sinx=cscx b)[(1+sinx)/ cosx] + [cosx/ (1+sinx)]= 2secx c) (sin^2x + 2sinx+1)/cos^2x= (1+sinx)/(1-sinx)

  • Math -

    You should memorize the following diagrams:

    1. the 30°-60°-90° triangle with matching sides
    1 -- √3 -- 2 (angles in radians, π/6 π/3 π/2)

    2. the 45° -- 45° -- 90° triangle with corresponding sides 1 -- 1 -- √2

    So sin π/4 or sin 45° = 1/√2


    arccos(-√3/2) = .....

    I know from looking at my triangle that cos60° or cosπ/3 = √3/2
    Also I know that the cosine is negative in II and III
    so arccos(-√3/2) = 180-60 = 120° or 2π/3

    cscØ = 2
    sinØ = 1/2
    Ø = 30° or π/6 , looking at my triangle

    With identities, it is usually a good idea to change all trig ratios to sines and cosines, and let the chips fall as they may.

    I will do the first one:

    LS = cotx cosx + sinx
    = (cosx/sinx)(cosx) + sinx
    = (cos^2 x + sin^2 x)/sinx
    = 1/sinx
    = csc x
    = RS

    try the others using that concept, let me know if you were successful.

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