9.2 f undamental t rigonometric i dentities and u sing a c alculator
TRANSCRIPT
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9.2 FUNDAMENTAL TRIGONOMETRIC IDENTITIES AND USING A CALCULATOR
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THE TRIGONOMETRIC FUNCTIONS
Osin
H
Acos
H
Otan
A
Hcsc
O
Hsec
A
Acot
O
SOHCAHTOA
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THE RECIPROCAL IDENTITIES
1sin
csc
1cos
sec
1tan
cot
1csc
sin
1sec
cos
1cot
tan
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THE QUOTIENT IDENTITIES
sintan
cos
cos
cotsin
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USE THE GIVEN INFORMATION TO FIND THE VALUE OF EACH OF THE FOUR REMAINING TRIGONOMETRIC FUNCTIONS.
2sin
5 21
cos5
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USE THE GIVEN INFORMATION TO FIND THE VALUE OF EACH OF THE FOUR REMAINING TRIGONOMETRIC FUNCTIONS.
2sin
3 5
cos3
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USING A CALCULATOR TO EVALUATE TRIGONOMETRIC FUNCTIONS Remember that when we evaluate
trigonometric functions: the input is the measure of an acute angle and
the output is the ratio of the lengths of the sides
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USING A CALCULATOR TO EVALUATE TRIGONOMETRIC FUNCTIONS For most acute angles, we approximate the
value of each of the trigonometric functions using a calculator.
Look for the keys on your calculator.
To evaluate csc, sec, and cot, we must use the reciprocal identity and/or the reciprocal keys on the calculator.
sin , cos , tan
1 x 1x
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USE A CALCULATOR TO FIND THE VALUE TO FOUR DECIMAL PLACES.
Scientific Calculator
Graphing
Calculator
sin30
30 cos cos 30 enter
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USE A CALCULATOR TO FIND THE VALUE TO FOUR DECIMAL PLACES.
Scientific Calculator
Graphing
Calculator
cot 45
45 tan 1 x 1tan 45 x
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USE A CALCULATOR TO FIND THE VALUE OF THE SIX TRIGONOMETRIC FUNCTIONS FOR THE GIVEN ANGLE TO FOUR DECIMAL PLACES.
25
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FIND THE MEASURE OF THE SIDE OF THE RIGHT TRIANGLE WHOSE LENGTH IS DESIGNATED BY A LOWERCASE LETTER. ROUND ANSWERS TO THE NEAREST WHOLE NUMBER.
64°
18x
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FIND THE MEASURE OF THE SIDE OF THE RIGHT TRIANGLE WHOSE LENGTH IS DESIGNATED BY A LOWERCASE LETTER. ROUND ANSWERS TO THE NEAREST WHOLE NUMBER.
19°
a
15