Trigonometric Ratios Triangles in Quadrant I

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Trigonometric RatiosTriangles in Quadrant I
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a Trig Ratio is

• a ratio of the lengths of two sides of a right
  ?

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3 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 Triangles

• The hypotenuse is opposite the right angle.
• The shortest side is opposite the smallest angle.
• The longest side is opposite the largest angle.

B
hypotenuse
a
A
b
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• Sin?
• Cos?
• Tan?

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Just remember Chief

• SOHCAHTOA

ine
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 a RECIPROCAL function.

• sine ? cosecant (csc)
• cosine ? secant (sec)
• tangent ? cotangent (cot)

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Six Trig Ratios of ? ?
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Find the ratios for the 6 trig functions.

• csc ? 13/5
• sec ? 13/12
• cot ? 12/5

• sin ? 5/13
• cos ? 12/13
• tan ? 5/12

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Find the ratios for the 6 trig functions.
Given csc ? 5/3

• csc ? 5/3
• sec ? 5/4
• cot ? 4/3

• sin ? 3/5
• cos ? 4/5
• tan ? 3/4

Use Pythagorean Theorem to find the missing side
length!
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Find the ratios for the 6 trig functions.
Given tana 4

• csc a
• sec a
• cot a

• sin a
• cos a
• tan a 4

Use Pythagorean Theorem to find the missing side
length!