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TODAY IN ALGEBRA 2.0… Review: Pythagorean Theorem Learning Target: Find all six trigonometric functions. Independent Practice

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Page 1: TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice

TODAY IN ALGEBRA 2.0…

Review: Pythagorean Theorem

Learning Target: Find all six trigonometric functions.

Independent Practice

Page 2: 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

Page 3: TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice

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:

Page 4: TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice

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:

Page 5: TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice

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:

Page 6: TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice

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)

Page 7: TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice

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

Page 8: TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice

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

Page 9: TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice

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

Page 10: TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice

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

Page 11: TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice

HOMEWORK #2:

Pg. 856: 3-7, 9-14

If finished, work on other assignments:

HW #1: Intro to TRIG WS