today in algebra 2.0… review: pythagorean theorem learning target: find all six trigonometric...
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TODAY IN ALGEBRA 2.0…
Review: Pythagorean Theorem
Learning Target: Find all six trigonometric functions.
Independent Practice
PYTHAGOREAN THEOREM:
h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑙𝑒𝑔
𝑙𝑒𝑔
𝑙𝑒𝑔2+𝑙𝑒𝑔2=h𝑦𝑝2
𝑥
3
5
PRACTICE: Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle.
The unknown side is attached to the right angle so it is a leg of the triangle.
Use the Pythagorean theorem to find the missing leg:
𝑥
913
PRACTICE: Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle.
The unknown side is attached to the right angle so it is a leg of the triangle.
Use the Pythagorean theorem to find the missing leg:
𝑥8
7
PRACTICE: Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in the simplest radical form.
The unknown side is not attached to the right angle so it is a hypotenuse of the triangle.
Use the Pythagorean theorem to find the missing leg:
TRIGONOMETRIC RATIOS:
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃
𝑺𝑰𝑵𝑬 :
𝑪𝑶𝑺𝑰𝑵𝑬 :
𝑻𝑨𝑵𝑮𝑬𝑵𝑻 :
𝒔𝒊𝒏𝜽=𝑶𝑯
𝒄𝒐𝒔 𝜽=𝑨𝑯
𝒕𝒂𝒏𝜽=𝑶𝑨
𝑪𝑶𝑺𝑬𝑪𝑨𝑵𝑻 :
𝑺𝑬𝑪𝑨𝑵𝑻 :
𝑪𝑶𝑻𝑨𝑵𝑮𝑬𝑵𝑻 :
𝒄𝒔𝒄 𝜽=𝑯𝑶
𝒔𝒆𝒄 𝜽=𝑯𝑨
𝒄𝒐𝒕 𝜽=𝑨𝑶
RECIPROCALS: (fractions flipped)
PRACTICE: Given the sides of the right triangle, find all six trigonometric ratios.
𝑠𝑖𝑛𝐵=𝑂𝐻
𝑐𝑜𝑠𝐵=𝐴𝐻
𝑡𝑎𝑛𝐵=𝑂𝐴
¿815
¿1215
¿812
𝑂𝐻
𝐴
15
12
8
¿45
¿23
𝐴 𝐵
𝐶
𝑐𝑠𝑐 𝐵=𝐻𝑂
𝑠𝑒𝑐 𝐵=𝐻𝐴
𝑐𝑜𝑡 𝐵=𝐴𝑂
¿158
¿54
¿32
PRACTICE: Given the sides of the right triangle, find all six trigonometric ratios.
𝑠𝑖𝑛 𝐴=𝑂𝐻
𝑐𝑜𝑠 𝐴=𝐴𝐻
𝑡𝑎𝑛 𝐴=𝑂𝐴
¿920
¿ √3320
¿9
√33
𝑂𝐻
𝐴√33
920
𝐴
𝐵
𝐶
𝑐𝑠𝑐𝐴=𝐻𝑂
𝑠𝑒𝑐𝐴=𝐻𝐴
𝑐𝑜𝑡𝐴=𝐴𝑂
¿209
¿20
√33¿ √339
4
𝑥 5
PRACTICE: Find the missing side then identify all six trigonometric functions.
𝑠𝑖𝑛𝜃=𝑂𝐻
𝑐𝑜𝑠𝜃=𝐴𝐻
𝜃
𝑡𝑎𝑛𝜃=𝑂𝐴
¿35
¿45
¿34
𝑂 𝐻
𝐴
3=¿
𝑐𝑠𝑐𝐴=𝐻𝑂
𝑠𝑒𝑐𝐴=𝐻𝐴
𝑐𝑜𝑡𝐴=𝐴𝑂
¿53
¿54
¿43
7
𝑥5
PRACTICE: Find the missing side then identify all six trigonometric functions.
𝑠𝑖𝑛𝜃=𝑂𝐻
𝑐𝑜𝑠𝜃=𝐴𝐻
𝜃
𝑡𝑎𝑛𝜃=𝑂𝐴
¿5
√74¿7
√74¿57
𝑂𝐻
𝐴
¿√74
𝑐𝑠𝑐𝐴=𝐻𝑂
𝑠𝑒𝑐𝐴=𝐻𝐴
𝑐𝑜𝑡𝐴=𝐴𝑂
¿ √745
¿ √747
¿75
HOMEWORK #2:
Pg. 856: 3-7, 9-14
If finished, work on other assignments:
HW #1: Intro to TRIG WS
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