Part I Finding Values for Trig Functions

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Presentation transcript:

Part I Finding Values for Trig Functions Sin = opposite ÷ hypotenuse Cos = adjacent ÷ hypotenuse Tan = opposite ÷ adjacent Opposite Hypotenuse θ Adjacent Tim Glahn LCJVS Mathematics Dept.

θ 13 in 5 in 12 in Find cos <θ = Tim Glahn LCJVS Mathematics Dept.

θ 13 in 5 in 12 in Find sin <θ = Tim Glahn LCJVS Mathematics Dept.

θ 13 in 5 in 12 in Find tan <θ = Tim Glahn LCJVS Mathematics Dept.

Practice Tim Glahn LCJVS Mathematics Dept.

Remember……. θ Hypotenuse Opposite Adjacent Tim Glahn LCJVS Mathematics Dept.

Find the sin <α 20 in 12in 15 in <β <α Tim Glahn LCJVS Mathematics Dept.

Find the cos <β 13 in 12in 5 in <β <α Tim Glahn LCJVS Mathematics Dept.

Find the sin <α 13 in 12in 5 in <β <α Tim Glahn LCJVS Mathematics Dept.

Find the sin <β <β 20 in 12in <α 15 in Tim Glahn LCJVS Mathematics Dept.

Find the tan <α <β 13 in 12in <α 5 in Tim Glahn LCJVS Mathematics Dept.

Find the tan <β <β 20 in 12in <α 15 in Tim Glahn LCJVS Mathematics Dept.

Find the cos <α <β 13 in 12in <α 5 in Tim Glahn LCJVS Mathematics Dept.

Find the tan <β <β 17 in 16in <α 5 in Tim Glahn LCJVS Mathematics Dept.

Find the tan <β <β 13 in 12in <α 5 in Tim Glahn LCJVS Mathematics Dept.

Find the cos <α <β 20 in 12in <α 15 in Tim Glahn LCJVS Mathematics Dept.

Find the cos <α <β 13 in 12in <α 5 in Tim Glahn LCJVS Mathematics Dept.

Find the sin <β <β 13 in 12in <α 5 in Tim Glahn LCJVS Mathematics Dept.

Find the tan <α <β 13 in 12in <α 5 in Tim Glahn LCJVS Mathematics Dept.

Find the tan <α <β 20 in 12in <α 15 in Tim Glahn LCJVS Mathematics Dept.

Find the tan <β <β 20 in 12in <α 15 in Tim Glahn LCJVS Mathematics Dept.

Find the sin <α 16in 5 in <β 17 in <α Tim Glahn LCJVS Mathematics Dept.

Find the cos <β <β 17 in 16in <α 5 in Tim Glahn LCJVS Mathematics Dept.

Find the sin <β <β 17 in 16in <α 5 in Tim Glahn LCJVS Mathematics Dept.

Find the cos <β <β 20 in 12in <α 15 in Tim Glahn LCJVS Mathematics Dept.

Part II Finding Angles Using Trig Functions Use the arc sin, arc cos, and arc tan functions to find angles. Sin-1 Cos-1 and Tan-1 are how they appear on your Calculator Any two sides can be used to find an angle measure. Tim Glahn LCJVS Mathematics Dept.

Which Arc Function Do I Use? If you have opposite and hypotenuse use the arc sin or sin-1. If you have adjacent and hypotenuse use the arc cos or cos-1 If you have opposite and adjacent use the arc tan or tan-1 Tim Glahn LCJVS Mathematics Dept.

Finding an Angle Use Sin-1 θ = Sin-1(15/31) = 28º56’ 31 15 θ hypotenuse 31 15 Opposite θ Use Sin-1 θ = Sin-1(15/31) = 28º56’ Tim Glahn LCJVS Mathematics Dept.

Use Cos-1 θ = Cos-1(22/31) = 44º 47’ 31 θ 22 hypotenuse Adjacent Tim Glahn LCJVS Mathematics Dept.

Use Tan-1 θ = Tan-1(15/22) = 34º17’ 15 θ 22 Opposite Adjacent Tim Glahn LCJVS Mathematics Dept.