Trignonmetry

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Please find the exact values:

Tan(-3p/4)=

Sec(2p/3)=

Csc(7p/4)=

Cot(11p/6)=

p=pie

  • Trignonmetry -

    -3pi/4 = 2pi -3pi/4 = + 5 pi/4
    so you really want tan 5pi/4 which is pi/4 below the -y axis
    x = -1
    y = -1
    y/x = tangent = 1

    sec 2 pi/3 = 1/cos 2 pi/3
    that angle is between pi/2 and pi, second quadrant
    pi - 2 pi/3 = pi/3 above -y axis
    x = -1
    y = +sqrt 3
    sqrt(x^2+y^2) = hypotenuse = 2
    so
    cos(2pi/3) = -1/2
    sec(2 pi/3)= -2

    etc. draw the triangles

  • Trignonmetry -

    You should be familiar with the trig ratios of the 30-60-90º triangle as well as the 45-45-90º triangle
    pi/4 radians <-----> 45º
    pi/3 radians <-----> 60º
    pi/6 radians <-----> 30º

    all your given angles are multiples of these.

    I will do the last one
    cot(11pi/6) = 1/tan(11pi/6)

    11pi/6 is in the fourth quadrant, in the fourth quadrant the tangent is negative, so the cotangent is negative.

    The angle is pi/6 away from the x-axis, so the 'angle in standard position' is pi/6
    tan pi/6 = 1/√3, so cot pi/6 = √3

    then cot(11pi/6) = -√3

    do the others the same way.

  • Trignonmetry -

    What is sin of 660?
    And
    What is csc(-2pi)/3?

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