Post on 30-Dec-2015
transcript
Warm-Up 3/24-25What are three basic trigonometric functions and the their ratios?
Sine: sin
Cosine: cos
Tangent: tan
ΒΏπππhπ¦π
ΒΏπππhπ¦π
ΒΏππππππ
Rigor:You will learn how to solve right triangles, and find the three basic trigonometric ratios. Relevance:You will be able to solve real world problems using trigonometric ratios.
Special Right Triangles45α΅- 45α΅- 90α΅: both legs are congruent and the length of the hypotenuse is times the length of a leg.
30α΅- 60α΅- 90α΅: The length of the hypotenuse is 2 times the shorter leg and the other leg is times the shorter leg.
π =πππ hπππππ‘
h=hπ¦πππ‘πππ’π π=π β2
π = hπ πππ‘ πππh=hπ¦πππ‘πππ’π π=2π π=πππππππ=π β3
60α΅
30α΅
x
16 345α΅
x
x
Example 1: Solve the triangles.
a. b.
12=π₯ β212
β2=π₯
β2β2β
12β22
=π₯
6 β2=π₯
s
16β3=π β316=π
π₯=2π π₯=2(16 )π₯=32
Since any two right triangles with angle are similar, side ratios are the same, regardless of the size of the triangle.
3
4
530
40
50
2 10
ΞΈ
3
7
Example 2: Find the exact values of the 3 basic Trigonometric functions of
s πππ=πππhπ¦π
ΒΏ 2β107
oppadj
hyp
cosπ=πππhπ¦π
ΒΏ37
taππ=ππππππ
ΒΏ 2β103
Example 3: If , find the exact values of the 2 remaining basic trigonometric functions.
1
2β2
3
s πππ=13=πππhπ¦π
12+π2=32
1+π2=9π2=8π=β8ΒΏ 2β2
3
ΒΏ 12β2
=β24
cosπ=πππhπ¦π
taππ=ππππππ
Example 4: 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
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
s πππ=1215.7
π=π ππβ1( 1215.7 )
πβ50Β°
Checkpoints:
3. Find the measure of .2. Find the value of .
1. Fill out chart with exact values.
12β32
β33
12
β32
β3
β22β22
1
sin 53 Β°=15π₯
π₯=15
sin 53 Β°
π₯=18.7820
cosπ=512
π=cosβ 1( 512 )π=65 Β°