Transcript Activity 4-1: The Radian Measure

Activity 4-2: Trig Ratios of Any Angles
Part 2: Trigonometric Ratios and Reciprocal
Trigonometric Ratios
Activity 4-2: Trig Ratios of Any Angles
Part 2: Trigonometric Ratios and Reciprocal
Trigonometric Ratios
•The reciprocal trigonometric ratios are the reciprocal of the primary ratios:
Primary Ratio
Reciprocal Ratio
Sine Ratio
sinθ = opposite/hypotenuse
sinθ = y/r
Cosecant Ratio
cscθ =hypotenuse/opposite
cscθ = r/y
Cosine Ratio
cosθ = adjacent/hypotenuse
cosθ = x/r
Secant Ratio
secθ =hypotenuse/adjacent
secθ = r/x
Tangent Ratio
tanθ = opposite/adjacent
tanθ = y/x
Cotangent Ratio
cotθ =opposite/adjacent
cotθ = x/y
Activity 4-2: Trig Ratios of Any Angles
Part 2: Trigonometric Ratios and Reciprocal
Trigonometric Ratios
•Let us try the following:
•Find the trigonometric and the reciprocal trigonometric ratios for θ = 7π/6
Step 1: Draw the angle on
your unit circle.
Since the denominator is 6,
every π (180o) is broken
into 6 parts.
3π/6
y
4π/6
2π/6
QUADRANT 2
QUADRANT 1
5π/6
π/6
θ
Step 2: Find your ratios.
Remember that the angle is
in the THIRD QUADRANT
therefore, only TANGENT
and COTENGENT are
POSITIVE
Step 2: Remember to
change your calculator to
radians. REMEMBER, your
calculator may not give the
proper sign. Use your
drawn angle.
sin (7π/6) = -0.5
csc (7π/6) = 1/-0.5 = 2
x
6π/6
7π/6
QUADRANT 3
TANGENT POSITIVE
cos (7π/6) = -0.866
sec (7π/6) = 1/-0.866 = -1.15
QUADRANT 4
tan (7π/6) = 0.577
cot (7π/6) = 1.73
Activity 4-2: Trig Ratios of Any Angles
Part 2: Trigonometric Ratios and Reciprocal
Trigonometric Ratios
•Example 1) Find the trigonometric and reciprocal trigonometric ratio for the
following angles. Try to solve before clicking to find the answer.
b) 3π/4
a) 2 rads
c) 11π/6
y
y
y
x
x
x
sin (2 rads) = 0.909
csc (2 rads) = 1.10
sin (3π/4 rads) = 0.707
csc (3π/4 rads) = 1.414
sin (11π/6 rads) = -0.5
csc (11π/6 rads) = -2
cos(2 rads) = -0.416
sec(2 rads) = -2.40
cos(3π/4 rads) = -0.707
sec(3π/4 rads) = -1.414
cos(11π/6 rads) = 0.866
sec(11π/6 rads) = 1.155
tan (2 rads) = -2.19
cot (2 rads) = -0.458
tan (3π/4 rads) = -1
cot (3π/4 rads) = -1
tan (11π/6 rads) = -0.577
cot (11π/6 rads) = -1.732