Comments (8) on “Use the angle in the unit circle to find the value of the three trigonometric functions below.”

  6. QUESTION 1

    For this first question, we need to measure the angle from the positive x-axis up to the terminal side, which is in the second quadrant.

    The measure of the angle

    [tex]= 90 + 55[/tex]
    [tex]= 145 \degree[/tex]

    The correct answer is A.

    QUESTION 2

    First let us find the acute angle in the fourth quadrant.

    This is given by
    [tex]\tan( \theta) = \frac{ \frac{1}{2} }{ \frac{ \sqrt{3} }{2} }[/tex]

    This implies that,

    [tex]\tan( \theta) =\frac{1}{ \sqrt{3} }[/tex]

    [tex]\theta=arctan(\frac{1}{ \sqrt{3} })[/tex]
    [tex]\theta=30 \degree[/tex]

    The angle in standard position
    [tex]=( 360 - \theta) \degree[/tex]
    [tex]= 330 \degree[/tex]

    We measure from the positive x-axis in the anticlockwise direction.

    The correct answer is B.

    QUESTION 3

    Coterminal angles are angles in standard position that have the same terminal side.

    To find angles that are coterminal with
    [tex]- 110 \degree[/tex]

    We either add or subtract 360°.

    Since we want the to be between 0° and 360°, we have to add 360° to get,

    [tex]- 110 + 360 = 250 \degree[/tex]

    The correct answer is A.

    QUESTION 4

    The acute angle that
    [tex]210 \degree[/tex]

    makes with the x-axis is 30°.

    Since 210 is in the third quadrant, both the sine and cosine ratio are negative.

    This implies that,

    [tex]\cos(210 \degree) = - \cos(30 \degree)[/tex]

    [tex]\sin(210 \degree) = - \sin(30 \degree)[/tex]

    Using the special angles,

    [tex]\cos(210 \degree) = - \frac{ \sqrt{3} }{2}[/tex]

    [tex]\sin(210 \degree) = - \frac{1}{2}[/tex]

    Or

    [tex]\cos(210 \degree) = - 0.87[/tex]

    [tex]\sin(210 \degree) = - 0.5[/tex]

    The correct answer is D.

    QUESTION 5

    The acute angle that 120° makes with the x-axis is 60°.

    Since 120° is in the second quadrant, the sine ratio is positive.

    This implies that,

    [tex]\sin(120 \degree) = \sin(60 \degree)[/tex]

    Using special angles, the exact value is,

    [tex]\sin(120 \degree) = \frac{\sqrt{3}}{2}[/tex]

    The correct answer is A.

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