Download Section 5.2: The Trigonometric Ratios

Section 5.2: The Trigonometric Ratios
August 21 & 24, 2015
5­2: Trigonometric Ratios in a Right Triangle
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• Trigonometry is all about comparing the lengths of two sides of a triangle. • When you compare two numbers, that is a ratio.
adjacent
Hypotenuse ­ side opposite the right angle
Opposite ­ leg opposite the reference angle
Adjacent ­ leg next to the reference angle
The 6 Trigonmetric Ratios!
Cosine
Secant
cosθ = adj/hyp secθ = 1/cosθ = hyp/adj Tangent
Cotangent
tanθ = opp/adj cotθ = 1/tanθ = adj/opp SOH­CAH­TOA
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sinθ = opp/hyp cscθ = 1/sin θ = hyp/opp
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Cosecant
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Sine
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Reciprocal Trigonometric Functions
(these are just flipped)
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Trigonometric Functions adjacent
θ
θ
Section 5.2: The Trigonometric Ratios
August 21 & 24, 2015
Find the value of the requested function
1.
2.
3.
4.
5. Find the values of the six trigonometric functions for angle A
C
8cm
B
15cm
A
Pythagorean Theorem
In a right triangle, the sum of the 2 legs squared is equal to the hypotenuse squared.
a2 + b2 = c2
Section 5.2: The Trigonometric Ratios
August 21 & 24, 2015
6. Find the values of the six trigonometric functions for angle B
C
18m
B
33m
A
7.) If cos θ = 2/3, find sec θ
8.) If the csc θ = 1.345, find sin θ
Section 5.2: The Trigonometric Ratios
August 21 & 24, 2015
9. Are the ratios limited as to how big or small they can be?
10. Is it possible for sin θ = 5/2?
11. Is it possible for csc θ = 4/9
Using your calculator, find the trigonometric ratio rounded to the nearest ten­thousandth.
12. sin 40° 13. cos 75°
14. tan 20°
Reciprocals...flip the function
15. csc 65° 16. sec 35°
17. cot 67°