Sec(x) = -1.5 trig help?

Sec(x) = -1.5, pi/2 and pi

find the remaining trig ratios, sin, cos, tan, cot, csc

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  • Lucy
    Lv 7
    1 decade ago
    Favorite Answer

    Given: sec x = -1.5 = -3 / 2

    Remember sec x = 1 / cos x = 1 / (adjacent / hypotenuse) = (hypotenuse / adjacent).

    Draw a diagram.

    .......|\...../|\

    .....x|..\..3|

    .......|....\..|

    <-----|------\|------------->

    .........-2...|

    ...............|

    ..............\|/

    Remember the Pythagorean Theorem.

    a² + b² = c² (where a and b are legs and c is the hypotenuse)

    Apply the formula.

    a² + b² = c²

    (-2)² + x² = 3²

    4 + x² = 9

    x² = 9 - 4

    x² = 5

    √(x²) = ± √5

    x = ± √5

    From the diagram, x is positive.

    x = √5 = opposite

    Remember that sin = opposite / hypotenuse.

    sin x = (√5 / 3)

    Remember that cos x = 1 / sec x.

    cos x = 1 / (-3 / 2) = (-2 / 3)

    Remember that tan = sin / cos.

    tan x = (√5 / 3) / (-2 / 3) = (-√5 / 2)

    Remember that cot = 1 / tan.

    cot x = 1 / (-√5 / 2) = (-2 / √5) = (-2 / √5)(√5 / √5) = (-2√5 / 5)

    Remember that csc = 1 / sin.

    csc x = 1 / (√5 / 3) = (3 / √5) = (3 / √5)(√5 / √5) = (3√5 / 5)

    ~~~~~~~~~~~~~~~~~~~~~~

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