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Sine Cosine Tangent
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Sine/Cosine/Tangent
Focus: Find out who is sohacahtoa and why is the
spelling of his name so important?
sohcahtoa
• SOHCAHTOA was the chief of the Trigonometric Tribe. He was a very wise man and people would go to him to solve their most pressing problems. Legend has it that he is the grandson of Sacajewea, for whom a famous park was erected in SW Washington state in time for Lewis and Clark to have a bath.
sohcahtoa
• SOHCAHTOA, a contemporary of Pythagorus, worked on finding ways to solve lengths and distances on right triangles.
• SOHCAHTOA is a famous dead mathematician, but his name lives on in legendary brilliance, he is still alive and working with roots.
• Spell his name correctly and you will certain pass into the tribe of Trigonometry’s lore.
Right Triangles’ Sides
• Hypotenuse• Adjacent side• Opposite side
• The adjacent and opposite sides are relative terms, compared to the location of the angle in question.
• The hypotenuse is always across from the right angle in a triangle.
Where they are found.
25°
Where the hypotenuse is found.hypotenuse
25°
Where the adjacent and opposite sides are found.
hypotenuse
25°
opposite
Adjacent means next to or attached. This will be shown on the next slide.
Where the adjacent and opposite sides are found.
hypotenuse
25°
Adjacent side to the25° angle.
Adjacent means next to or attached. The next slidewill show the relationships from the remaining angle.
Opposite the 25°angle.
Where the adjacent and opposite sides are found relative to the third
angle..
hypotenuse65°
Adjacentside
Adjacent means next to or attached. The hypotenuse isstill (always) across from the right angle.
Opposite the 65 degree angle.
Ratios
• Sine ratio:– Opposite over
hypotenuse
• Cosine ratio:– Adjacent over
hypotenuse
• Tangent ratio:– Opposite over
Adjacent
9
12
15
Trigonometry is based on the following relationships.
x°
Ratios
• Sine ratio:– Opposite over
hypotenuse9
12
15
x°9
15
Ratios
• Sine ratio:– Opposite over
hypotenuse
• Cosine ratio:– Adjacent over
hypotenuse
9
12
9
12
15
x°
12
15
Ratios
• Sine ratio:– Opposite over
hypotenuse
• Cosine ratio:– Adjacent over
hypotenuse
• Tangent ratio:– Opposite over
Adjacent
9
15
9
12
15
x°9
12
12
15
Ratios
• Sine ratio:– Opposite over
hypotenuse
• Cosine ratio:– Adjacent over
hypotenuse
• Tangent ratio:– Opposite over
Adjacent
9
12
15
Trigonometry charts are usually found at the back of math textbooks.Is there one in your book on page 668?
x°9
15
9
12
12
15 We can use these fractions as division statements and compare
the resulting answers to determinethe angle’s measurement.
What is the missing angle measurement?
.8000
9
15
9
12
12
15
.6000
.7500
