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.
Trigonometry
What do you remember?
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.
4-1a Right Triangle Trigonometry
Trigonometric Ratios: ratios of sides of a right triangle.
opposite
adjacent
hypotenuse
opp
adjhyp
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 𝜃=h𝑦𝑝𝑜𝑝𝑝
¿1sin 𝜃
∙
1h𝑦𝑝1h𝑦𝑝
=¿1
𝑜𝑝𝑝h𝑦𝑝
csc 𝜃=1sin 𝜃
Reciprocal Functions
sec𝜃=1
𝑐𝑜𝑠𝜃
cot 𝜃=1tan 𝜃
cot 𝜃=cos𝜃sin𝜃
tan𝜃=si n 𝜃cos𝜃
2 10
θ
3
7
Example 1: Find the exact values of the 6 Trigonometric functions of
s 𝑖𝑛𝜃=𝑜𝑝𝑝h𝑦𝑝
¿ 2√107
oppadj
hyp
cos𝜃=𝑎𝑑𝑗h𝑦𝑝
¿37
ta𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗
¿ 2√103
cs𝑐 𝜃=h𝑦𝑝𝑜𝑝𝑝
¿7
2√10¿ 7√1020
se𝑐 𝜃=h𝑦𝑝𝑎𝑑𝑗
¿73
𝑐𝑜𝑡 𝜃=𝑎𝑑𝑗𝑜𝑝𝑝
¿3
2√10¿ 3√1020
Trigonometric Ratios: ratios of sides of a right triangle.
opposite
adjacent
hypotenuse
opp
adjhyp
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 𝜃=h𝑦𝑝𝑜𝑝𝑝
¿1sin 𝜃
∙
1h𝑦𝑝1h𝑦𝑝
=¿1
𝑜𝑝𝑝h𝑦𝑝
csc 𝜃=1sin 𝜃
Reciprocal Functions
sec𝜃=1
𝑐𝑜𝑠𝜃
cot 𝜃=1tan 𝜃
cot 𝜃=cos𝜃sin𝜃
tan𝜃=si n 𝜃cos𝜃
2 10
θ
3
7
Example 1: Find the exact values of the 6 Trigonometric functions of
s 𝑖𝑛𝜃=𝑜𝑝𝑝h𝑦𝑝
¿ 2√107
oppadj
hyp
cos𝜃=𝑎𝑑𝑗h𝑦𝑝
¿37
ta𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗
¿ 2√103
cs 𝑐 𝜃=h𝑦𝑝𝑜𝑝𝑝
¿7
2√10¿ 7√1020
se𝑐 𝜃=h𝑦𝑝𝑎𝑑𝑗
¿73
𝑐𝑜𝑡 𝜃=𝑎𝑑𝑗𝑜𝑝𝑝
¿3
2√10¿ 3√1020
Example 2: If , find the exact values of the 5 remaining trigonometric functions.
1
2√2
3
s 𝑖𝑛𝜃=13=𝑜𝑝𝑝h𝑦𝑝
12+𝑏2=32
1+𝑏2=9𝑏2=8𝑏=√8¿ 2√2
3
¿ 12√2
=√24
¿31=3
¿ 32√2
=3√24
¿ 2√21
=2√2
cos𝜃=𝑎𝑑𝑗h𝑦𝑝
ta𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗
cs 𝑐 𝜃=h𝑦𝑝𝑜𝑝𝑝
se𝑐 𝜃=h𝑦𝑝𝑎𝑑𝑗
𝑐𝑜𝑡 𝜃=𝑎𝑑𝑗𝑜𝑝𝑝
Example 3: Find the value of . Round to the nearest tenth, if necessary.
x
°
7
cos𝜃=𝑎𝑑𝑗h𝑦𝑝
adj
hyp
cos 35 °=𝑥7
7 ∙cos35 °=𝑥7∙7
7 ∙cos35 °=𝑥Make sure your calculator is in degrees.
𝑥=5.73406431
𝑥≈5.7
or
sec 35 °=7𝑥
𝑥 ∙ s ec35 °=7𝑥¿
7sec 35 °
𝑥¿7¿¿ ¿
Example 5: Use a trigonometric function to find the measure of . Round to the nearest degree.
1215.7
opp
hyp
𝜃=49.84753016 °
𝜃
s 𝑖𝑛𝜃=𝑜𝑝𝑝h𝑦𝑝
not
s 𝑖𝑛𝜃=1215.7
𝜃=𝑠𝑖𝑛−1( 1215.7 )
𝜃≈50°
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 𝑖𝑛𝜃=𝑜𝑝𝑝h𝑦𝑝
¿513
cos𝜃=𝑎𝑑𝑗h𝑦𝑝
¿1213
ta𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗
¿512
cs𝑐 𝜃=h𝑦𝑝𝑜𝑝𝑝
¿135
se𝑐 𝜃=h𝑦𝑝𝑎𝑑𝑗
¿1312
𝑐𝑜𝑡 𝜃=𝑎𝑑𝑗𝑜𝑝𝑝
¿125
s 𝑖𝑛𝜃=1
√5¿ √55
cos𝜃=2
√5 ¿ 2√55
ta𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗¿12
cs 𝑐 𝜃=√51 ¿√5
se𝑐 𝜃=√52
𝑐𝑜𝑡 𝜃=21¿21
2
√5
s 𝑖𝑛53 °=15𝑥
𝑥 s 𝑖𝑛53 °=15𝑥¿
15sin 53 °
𝑥≈18.7820
s 𝑖𝑛𝜃=1416
θ ¿ sin−1( 1416 )θ≈61.0450 °
θ≈61 °
√−1math!
4-1a Assignment: TX p227, 3-36 DB3
Quiz Thursday 5/14
