Transcript Finding Trigonometric Ratios in a Right Triangle

Sine, Cosine, and Tangent
 A useful pneumonic: SOHCAHTOA!
 This pneumonic tells you how to find each ratio based on
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the side lengths of a right triangle.
Sin = Opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent
Adjacent refers to the leg adjacent to the angle in question.
Opposite refers to the leg opposite the angle in question.
Hypotenuse refers to the hypotenuse.
Sin, Cos, and Tan on a Triangle
 Sin (A)
= opposite/hypotenuse
= b/c
 Cos(A)
= adjacent/hypotenuse
= a/c
 Tan(A)
= opposite/adjacent
= b/a
Can you tell what the ratios
would be for angle C?
Secant, Cosecant, and Cotangent
 Easiest to remember in relation to the other three.
 Sec(x)
= 1/cos(x)
= hypotenuse/adjacent
 Csc(x)
= 1/sin(x)
= hypotenuse/opposite
 Cot(x)
= 1/tan(x)
= adjacent/opposite
Sec, Csc, and Cot on a Triangle
 Sec(A)
= hypotenuse/adjacent
= c/a
 Csc(A)
= hypotenuse/opposite
= c/b
 Cot(A)
= adjacent/opposite
= a/b
Can you tell what the ratios
would be for angle C?
Try it yourself!
What are the values of the
six trigonometric ratios
for angle A in this
triangle?
Answers
Sin(A)
= Opposite / Hypotenuse
= 4/5
Cos (A)
= Adjacent / Hypotenuse
= 3/5
Tan (A)
= Opposite / Adjacent
= 4/3
Sec(A)
= Hypotenuse / Adjacent
= 5/3
Csc(A)
= Hypotenuse / Opposite
= 5/4
Cot(A)
= Adjacent / Opposite
= 3/4