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5-2 Length of Arcs and Areas of Sectors   5-3 Trigonometric Ratios of Acute Angles    Quotes

5-2 Lengths of Arcs and Areas of Sectors

Circular Arc Length Formula  Circular sector area Formula

Circular Arc Length Formula

S = R(Theta)

s- arc length                                                          

r- radius

theta - radians

Find the length of the arc of the above diagram.

     S = R(theta)

        = 4 x (pie)/3

        = 4(pie)/3

Circular Sector Area Formula

       A = 1/2R²(theta)

A- area

R- radius

theta - radians

Find the area of the arc in the above diagram

    A = 1/2R²(theta)

    A = 1/2(4/1)² (pie)/3

        = (pie)/24

5-3 Trigonometric Ratios of Acute Angles

Basic trigonometric ratios     Finding ratios and angles

Basic trigonometric ratios:

Ancient Greeks, such as Hipparchus used ratios to find the length of sides and measurements of angles of right triangles. (Foresman)  Three ratios they used , called trigonometric ratios, were:

• sin - side opposite/hypotenuse
• cos - side adjacent/hypotenuse
• tan - side opposite/side adjacent

An easy way to remember what each ratio is is by SohCahToa.

• soh = sin-opp/hyp
• Coa = cos adj/hyp
• tan = opp/adj

Finding ratios and angles

Find sin B    (see above diagram)

        sin B = 2/5

To find the measurement of angle B, use the inverse of sin. (sin^-1)

    sin^-1B= 2/5 

               = 23.578 degrees

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