Notes Chapter 8.3

Trigonometry  A trigonometric ratio is a ratio of the side lengths of a right triangle.  The trigonometric ratios are:  Sine: opposite side over hypotenuse (SOH)  Cosine: adjacent side over hypotenuse (CAH)  Tangent: opposite side over adjacent side (TOA) Trigonometric ratios

Trigonometry  The trigonometric ratios are:  Sine: opposite side over hypotenuse (SOH)  Cosine: adjacent side over hypotenuse (CAH)  Tangent: opposite side over adjacent side (TOA) Trigonometric ratios  In the adjacent diagram, what side is opposite angle B? What side is adjacent (next to) to angle B?  What about angle C? Is it treated differently? Yes, because it is 90°!  In the diagram below, what side is opposite angle A? What side is adjacent (next to) to angle A? Remember that they hypotenuse is special and will never be an “opposite” or “adjacent” side.

Visualizing the information  The relative terms “opposite” and “adjacent” apply to any angle. It does not matter how the triangle is drawn. Remember, though, that the hypotenuse is always opposite the right (90°) angle.

Identifying opposite and adjacent sides  Can you identify which side is “opposite” and which side is “adjacent” for the given angles?  Which side is opposite for angle X? Which side is adjacent?  Which side is opposite for angle Y? Which side is adjacent?  Which side is the hypotenuse?

Identifying opposite and adjacent sides  Can you identify which side is “opposite” and which side is “adjacent” for the given angles?  Which side is opposite for angle P? Which side is adjacent?  Which side is opposite for angle Q? Which side is adjacent?  Which side is the hypotenuse?

Identifying opposite and adjacent sides  Can you identify which side is opposite and which side is adjacent for the given angles? Which side is the hypotenuse?  What side is side “a”? (Hold up the index card for your answer.)  What side is side “b”? (Hold up the index card for your answer.)  What side is side “c”? (Hold up the index card for your answer.) For angle A:

Identifying opposite and adjacent sides  Can you identify which side is opposite and which side is adjacent for the given angles? Which side is the hypotenuse?  What side is side “a”? (Hold up the index card for your answer.)  What side is side “b”? (Hold up the index card for your answer.)  What side is side “c”? (Hold up the index card for your answer.) For angle B:

Identifying opposite and adjacent sides  Can you identify which side is opposite and which side is adjacent for the given angles? Which side is the hypotenuse?  What side is side “o”? (Hold up the index card for your answer.)  What side is side “m”? (Hold up the index card for your answer.)  What side is side “n”? (Hold up the index card for your answer.) For angle M :

Identifying opposite and adjacent sides  Can you identify which side is opposite and which side is adjacent for the given angles? Which side is the hypotenuse?  What side is side “o”? (Hold up the index card for your answer.)  What side is side “m”? (Hold up the index card for your answer.)  What side is side “n”? (Hold up the index card for your answer.) For angle O :

Identifying opposite and adjacent sides  Can you identify which side is opposite and which side is adjacent for the given angles? Which side is the hypotenuse?  What side is side “b”? (Hold up the index card for your answer.)  What side is side “a”? (Hold up the index card for your answer.)  What side is side “c”? (Hold up the index card for your answer.) For angle B :

Identifying opposite and adjacent sides  Can you identify which side is opposite and which side is adjacent for the given angles? Which side is the hypotenuse?  What side is side “b”? (Hold up the index card for your answer.)  What side is side “a”? (Hold up the index card for your answer.)  What side is side “c”? (Hold up the index card for your answer.) For angle A :

Identifying opposite and adjacent sides  Can you identify which side is opposite and which side is adjacent for the given angles? Which side is the hypotenuse?  What side is side “b”? (Hold up the index card for your answer.)  What side is side “a”? (Hold up the index card for your answer.)  What side is side “c”? (Hold up the index card for your answer.) For angle C :

Identifying opposite and adjacent sides  Can you identify which side is opposite and which side is adjacent for the given angles? Which side is the hypotenuse?  What side is side “b”? (Hold up the index card for your answer.)  What side is side “a”? (Hold up the index card for your answer.)  What side is side “c”? (Hold up the index card for your answer.) For angle D :

Trigonometry Trigonometric ratios

Trigonometry Trigonometric ratios

Trigonometry Trigonometric ratios

Trigonometry Trigonometric ratios

Trigonometry Trigonometric ratios

Trigonometry Trigonometric ratios

Trigonometry  The trigonometric ratios are: o Sine: opposite side over hypotenuse (SOH) o Cosine: adjacent side over hypotenuse (CAH) o Tangent: opposite side over adjacent side (TOA) Trigonometric ratios  If the lengths of a, b and c are 6, 8 and 10 what are the values of sine, cosine and tangent for angles A and B? Do you notice any patterns? What is Sin(A) and Cos(B)? What are Tan(A) and Tan(B)? o Sin(A) = a/c = 6/10 or 3/5 o Cos(A) = b/c = 8/10 or 4/5 o Tan(A) = a/b = 6/8 or 3/4 o Sin(B) = b/c = 8/10 or 4/5 o Cos(B) = a/c = 6/10 or 3/5 o Tan(B) = b/a = 8/6 or 4/3

Trigonometry Sine: opposite side over hypotenuse (SOH) Cosine: adjacent side over hypotenuse (CAH) Tangent: opposite side over adjacent side (TOA) Trigonometric ratios  If the lengths of a, b and c are 5, 7 and 10 what are the values of sine, cosine and tangent for A and B? Do you notice any patterns? What is Sin(A) and Cos(B)? What are Tan(A) and Tan(B)? o Sin(A) = a/c = 5/10 or 1/2 o Cos(A) = b/c = 7/10 o Tan(A) = a/b = 5/7 o Sin(B) = b/c = 7/10 o Cos(B) = a/c = 5/10 or 1/2 o Tan(B) = b/a = 7/5