required materials for class paper pencils eraser pens (black/blue) colored pencils graph paper...
TRANSCRIPT
Required Materials for ClassPaperPencils eraserPens (Black/Blue)Colored Pencils Graph Paper
3-ring binder, with dividers
Graphing CalculatorTI 84+ or TI 89
OrSpiral Notebook and Folder with clasps & pockets
OptionalBox of TissueHand Sanitizer
Skyward Mathwebb.com Class SuppliesTardiesLeaving ClassGrades for Assignments7 points: Assignment complete and on time6 points: Assignment completed but late5 points: Assignment completed but not turned in until the day of the test4 point: Assignment completed but not turned in until after the test0 points: Assignment not turned in.
Rigor:You will learn the six trigonometric
functions and how to use them to solve problems.
Relevance:
You will be able to solve real world right triangle trigonometry problems using the
six trigonometric functions.
6 Trigonometric Ratios:3 basic: 3 additional:
sin
cos
tan
opp
hyp
adj
hyp
opp
adj
csc
sec
cot
hyp
opp
hyp
adj
adj
opp
csc π=hπ¦ππππ
ΒΏ1sin π
β
1hπ¦π1hπ¦π
=ΒΏ1
πππhπ¦π
csc π=1sin π
Reciprocal Functions
secπ=1
πππ π
cot π=1tan π
cot π=cosπsinπ
tanπ=si n πcosπ
2 10
ΞΈ
3
7
Example 1: Find the exact values of the 6 Trigonometric functions of
s πππ=πππhπ¦π
ΒΏ 2β107
oppadj
hyp
cosπ=πππhπ¦π
ΒΏ37
taππ=ππππππ
ΒΏ 2β103
csπ π=hπ¦ππππ
ΒΏ7
2β10ΒΏ 7β1020
seπ π=hπ¦ππππ
ΒΏ73
πππ‘ π=ππππππ
ΒΏ3
2β10ΒΏ 3β1020
6 Trigonometric Ratios:3 basic: 3 additional:
sin
cos
tan
opp
hyp
adj
hyp
opp
adj
csc
sec
cot
hyp
opp
hyp
adj
adj
opp
Since any two right triangles with angle are similar, these ratios are the same, regardless of the size of the triangle.
3
4
530
40
50
csc π=hπ¦ππππ
ΒΏ1sin π
β
1hπ¦π1hπ¦π
=ΒΏ1
πππhπ¦π
csc π=1sin π
Reciprocal Functions
secπ=1
πππ π
cot π=1tan π
cot π=cosπsinπ
tanπ=si n πcosπ
2 10
ΞΈ
3
7
Example 1: Find the exact values of the 6 Trigonometric functions of
s πππ=πππhπ¦π
ΒΏ 2β107
oppadj
hyp
cosπ=πππhπ¦π
ΒΏ37
taππ=ππππππ
ΒΏ 2β103
cs π π=hπ¦ππππ
ΒΏ7
2β10ΒΏ 7β1020
seπ π=hπ¦ππππ
ΒΏ73
πππ‘ π=ππππππ
ΒΏ3
2β10ΒΏ 3β1020
Example 2: If , find the exact values of the 5 remaining trigonometric functions.
1
2β2
3
s πππ=13=πππhπ¦π
12+π2=32
1+π2=9π2=8π=β8ΒΏ 2β2
3
ΒΏ 12β2
=β24
ΒΏ31=3
ΒΏ 32β2
=3β24
ΒΏ 2β21
=2β2
cosπ=πππhπ¦π
taππ=ππππππ
cs π π=hπ¦ππππ
seπ π=hπ¦ππππ
πππ‘ π=ππππππ
Example 3: Find the value of . Round to the nearest tenth, if necessary.
x
Β°
7
cosπ=πππhπ¦π
adj
hyp
cos 35 Β°=π₯7
7 βcos35 Β°=π₯7β7
7 βcos35 Β°=π₯Make sure your calculator is in degrees.
π₯=5.73406431
π₯β5.7
or
sec 35 Β°=7π₯
π₯ β s ec35 Β°=7π₯ΒΏ
7sec 35 Β°
π₯ΒΏ7ΒΏΒΏ ΒΏ
Example 5: Use a trigonometric function to find the measure of . Round to the nearest degree.
1215.7
opp
hyp
π=49.84753016 Β°
π
s πππ=πππhπ¦π
not
s πππ=1215.7
π=π ππβ1( 1215.7 )
πβ50Β°
4-1a Checkpoints:
Find the measure of .Find the value of .
2. If , find the exact values of the five remaining trigonometric functions for the acute angle .
Find the exact values of the six trigonometric functions of .
s πππ=πππhπ¦π
ΒΏ513
cosπ=πππhπ¦π
ΒΏ1213
taππ=ππππππ
ΒΏ512
csπ π=hπ¦ππππ
ΒΏ135
seπ π=hπ¦ππππ
ΒΏ1312
πππ‘ π=ππππππ
ΒΏ125
s πππ=1
β5ΒΏ β55
cosπ=2
β5 ΒΏ 2β55
taππ=ππππππΒΏ12
cs π π=β51 ΒΏβ5
seπ π=β52
πππ‘ π=21ΒΏ21
2
β5
s ππ53 Β°=15π₯
π₯ s ππ53 Β°=15π₯ΒΏ
15sin 53 Β°
π₯β18.7820
s πππ=1416
ΞΈ ΒΏ sinβ1( 1416 )ΞΈβ61.0450 Β°
ΞΈβ61 Β°