right triangle trigonometry. degree mode v. radian mode
TRANSCRIPT
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Right Triangle Trigonometry
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Symbols
Theda – Represents the angle measure
Hypotenuse
Opposite Side
Adjacent
Side
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Six Trigonometric Ratios
3 Basic Ratios + 3 Reciprocal Ratios What is a reciprocal?
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Six Trigonometric Ratios, cont.
Basic Trig. Ratio Sine Cosine Tangent
Reciprocal Trig. Ratio Cosecant Secant Cotangent
It’s a sin to have two c’s.
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Three Basic Trig. Ratios
SOH-CAH-TOA
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Sine (SOH)
hypotenuse
oppositesin
24 25
7
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Cosine (CAH)
hypotenuse
adjacentcos
24 25
7
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Tangent (TOA)
adjacent
oppositetan
24 25
7
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Cosecant – Reciprocal of Sine
opposite
hypotenusecsc
24 25
7
sin
1csc
(“It’s a sin to have two C’s.”)
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Secant – Reciprocal of Cosine
adjacent
hypotenusesec 24 25
7
cos
1sec
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Cotangent – Reciprocal of Tangent
opposite
adjacentcot 24 25
7
tan
1cot
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Solving for Side Lengths
If given one side and one angle measure, then we can solve for any other side of the triangle.
8
x
65
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Solving Right Triangles, cont.
1. Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse?
2. Pick the appropriate trig function to solve for x.
3. Solve for x.
8
x
65
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Solving for Side Lengths, cont.
8
x
65
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Solving Side Lengths, cont.
7 x
30
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Inverse Trigonometric Functions
We can “undo” trig ratios Gives us the angle measurement (theta) Represented by a small –1 in the upper right hand
corner Ex.
2nd button → trig ratio
1sin
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Inverse Trigonometric Functions, cont.
60.cos
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Inverse Trigonometric Functions, cont.
Experiment: Take the sin–1(0.75) and the csc (0.75). What do you get?
**** sin –1 ≠ csc Ѳ !!!!! ****
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Your Turn: Solve for thetaRound to nearest hundredth
50.sin
50.cos 2
3sin
1tan
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Solving For Angle Measures
If given two sides of a triangle, then we can solve for any of the angles of the triangle.
54
θ
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Solving for Angle Measures, cont.
1. Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse?
2. Pick the appropriate trig function to solve for
3. Solve for using the inverse trigonometric function
54
θ
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Solving for Angle Measures, cont.
54
θ
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Your Turn:
Complete problems 1 – 6 in the Right Triangle Trigonometry Guided Notes – Part II packet.
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Answers
1. 2. 3.
4. 5. 6.