Trigo V2010 2

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16.1 POSI TIVE & NEG ATIV E AN GLES (a) Posi tiv e ang les – angles measured in the anticlockwise direction from the positive x-axis. (b) Neg ati ve ang les – a ngl es mea sur ed in the clockwise direction from the positive x-axis. Exercise 16.1 Represent each of the following angles in a unit circle. Then, state (i) the qua dra nt i n whic h t he a ngl es loc ate d, (ii) the corresponding acute angle. (a) 150 o (b) 315 o (c) 225 o (d)  6 (e) 3 2π   (f)  4 7π   16.2 (A) THE SIX TRIGONOMETRIC FUNCTIONS (i) sin θ = r  y if r = 1, then sin θ = y (ii) cos θ = r  x if r = 1, then cos θ = x  r  y (iii) tan θ =  x  y = θ θ cos sin   x (iv) cosec θ =  y r if r = 1, then cosec θ =  y 1 = θ sin 1 (v) sec θ =  x r if r = 1, then sec θ =  x 1 = θ cos 1 (vi) cot θ =  y  x = θ tan 1 = θ θ sin cos 16.2 (B) COMPLEMENT ANGLES (i) sin θ = cos (90 o  θ) (ii) cos θ = sin (90 o   θ) (i ii ) ta n θ = cot (90 o   θ) (i v) cosec θ = sec (90 o   θ) (v) sec θ = cosec (90 o   θ) θ

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Transcript of Trigo V2010 2

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    16.1 POSITIVE & NEGATIVE ANGLES

    (a) Positive angles angles measured in the

    anticlockwisedirection

    from the positive x-axis.

    (b) Negative angles angles measured in the clockwise directionfrom the positive x-axis.

    Exercise 16.1Represent each of the following angles in a unit circle. Then, state

    (i) the quadrant in which the angles located,

    (ii) the corresponding acute angle.

    (a) 150o (b) 315o (c) 225o

    (d) 6

    (e)3

    2

    (f) 4

    7

    16.2 (A) THE SIX TRIGONOMETRIC FUNCTIONS(i) sin =

    r

    yif r= 1, then sin =y

    (ii) cos =r

    xif r = 1, then cos =x r y

    (iii) tan =x

    y=

    cos

    sin x

    (iv) cosec =y

    r if r = 1, then cosec =y

    1 = sin1

    (v) sec =x

    rif r = 1, then sec =

    x

    1= cos

    1

    (vi) cot =y

    x= tan

    1=

    sin

    cos

    16.2 (B) COMPLEMENT ANGLES

    (i) sin = cos (90o )

    (ii) cos = sin (90o)

    (iii) tan = cot (90o)

    (iv) cosec = sec (90o)

    (v) sec = cosec (90o)

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    (vi) cot = tan (90o)

    16.2 (C) RELATIONSHIPS BETWEEN ANGLES > 90O

    AND ITS ACUTE ANGLES

    Quadrant II: Quadrant IV:sin = sin (180o) sin = sin (360o)

    cos = cos (180o) cos = cos (360o)

    tan = tan (180o) tan = tan (360o)

    Quadrant III: Note:sin ( 180o) = sin If is the corresponding acute

    cos ( 180o) = cos angle in the quadrant, then angle

    tan ( 180o) = tan in Quadrant III is (180 + ).

    16.2 (D) SPECIAL ANGLES: ( 0O, 30O, 45O, 60O, 90O, 180O, 270O, 360O)

    0O

    30O

    45O

    60O

    90O

    180O

    270O

    360O

    sin 02

    11 0 1 0

    cos 12

    10 1 0 1

    tan 0 1 0 0

    Exercise 16.2:

    1. Given that sin =5

    3, find the value of each of the following

    a) cos

    2

    QuadrantIII

    Tangent

    positive(180o)

    Quadrant IAll

    positive

    ( )

    QuadrantIV

    Cosinepositive

    (360o)

    QuadrantII

    Sinepositive

    (180o)

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    b) cosec

    c) tan

    d) cot

    2. Given cos

    =

    p and 180

    o