trigonometric ratios triangles in quadrant i
DESCRIPTION
Trigonometric Ratios Triangles in Quadrant I. a Trig Ratio is …. … a ratio of the lengths of two sides of a right Δ. 3 Basic Trig Ratios. Sine (sin) Cosine (cos) Tangent (tan). - PowerPoint PPT PresentationTRANSCRIPT
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TrigonometriTrigonometric Ratiosc Ratios
Triangles in Quadrant Triangles in Quadrant II
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a a Trig Ratio Trig Ratio is …is …
… a ratio of the lengths of two
sides of a right Δ
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3 Basic Trig Ratios3 Basic Trig Ratios
• Sine (sin)• Cosine (cos)
• Tangent (tan)These trig ratios (or trig
functions) can be used to SOLVE a right triangle … that means to find
all the side lengths and angle measures of the right triangle.
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Right TrianglesRight Triangles• The hypotenuse is opposite the right angle.• The shortest side is opposite the smallest angle.• The longest side is opposite the largest angle.
Ab
a
B
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• Sinϴ =
• Cosϴ =
• Tanϴ=
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
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Just remember Chief…Just remember Chief…SOHCAHTOAine
ppos i t e
ypo t enuse
osine
d j acen t
ypo t enuse
angent
ppos i t e
d j acen t
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Each trig function has Each trig function has a a RECIPROCALRECIPROCAL
function.function.• sine → cosecant (csc)• cosine → secant (sec)• tangent → cotangent (cot)
sinopp
hyp cos
adj
hyp tan
opp
adj
cschyp
opp sec
hyp
adj cot
adj
opp
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Six Trig Ratios of Six Trig Ratios of ϴϴ
siny
r
cosx
r
tany
x
ϴx
yr
cotx
y
secr
x
cscr
y
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Find the ratios for the 6 trig Find the ratios for the 6 trig
functions.functions.
sin ϴ = 5/13
cos ϴ = 12/13
tan ϴ = 5/12
ϴ
13
12
5
csc ϴ = 13/5
sec ϴ = 13/12
cot ϴ = 12/5
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Find the ratios for the 6 trig Find the ratios for the 6 trig
functions.functions.
sin ϴ = 3/5
cos ϴ = 4/5
tan ϴ = 3/4
ϴ csc ϴ = 5/3
sec ϴ = 5/4
cot ϴ = 4/3
Given: csc Given: csc ϴϴ = 5/3 = 5/3
Use Use PythagoreaPythagorean Theorem n Theorem to find the to find the
missing side missing side length!length!
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Find the ratios for the 6 trig Find the ratios for the 6 trig
functions.functions.
sin α =
cos α =
tan α = 4
α csc α =
sec α =
cot α =
Given: tanGiven: tanαα = 4 = 4
Use Use PythagoreaPythagorean Theorem n Theorem to find the to find the
missing side missing side length!length!