TODAY IN ALGEBRA 2.0…

Review: Pythagorean Theorem and the six trigonometric functions

Learning Target: 13.1 You will find missing sides of a triangle using TRIG

Independent Practice

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35

REVIEW: Given the sides of the right triangle, find all the trigonometric ratios.

𝑠𝑖𝑛𝐶=𝑂𝐻

𝑐𝑜𝑠𝐶=𝐴𝐻

𝑡𝑎𝑛𝐶=𝑂𝐴

𝐴

𝐵

𝐶

¿

¿

¿

𝑐𝑠𝑐𝐶=𝐻𝑂

𝑠𝑒𝑐𝐶=𝐻𝐴

𝑐𝑜𝑡 𝐶=𝐴𝑂

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¿

¿

35

4534

53

5443

𝑥

¿13

12

5

REVIEW: Given the sides of the right triangle, find all the trigonometric ratios.

𝑠𝑖𝑛𝐵=𝑂𝐻

𝑐𝑜𝑠 𝐵=𝐴𝐻

𝑡𝑎𝑛𝐵=𝑂𝐴

𝐴

𝐵

𝐶

¿

¿

¿

𝑐𝑠𝑐𝐵=𝐻𝑂

𝑠𝑒𝑐𝐵=𝐻𝐴

𝑐𝑜𝑡 𝐵=𝐴𝑂

¿

¿

¿

1213

513125

1312

135512

𝑥

MULTIPLY: when x is on topExample:

DIVIDE: when x is on bottomExample:

121

𝑛

EXAMPLE: Find n using the tangent ratio. Round answer to the nearest tenth.

52 °

Use tangent ratio

Substitute known values

Variable on top (multiply)

Solve for n using calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

𝑥5 4

PRACTICE: Find x using the tangent ratio. Round answer to the nearest tenth.

39 °

Use sine ratio Substitute known values Variable on bottom (divide)

Solve for x using a calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

67 𝑥

PRACTICE: Find x using the tangent ratio. Round answer to the nearest tenth.

46 °

Use sine ratio

Substitute known values

Variable on top (multiply)

Solve for x using calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

230

𝑥

PRACTICE: Find x using the tangent ratio. Round answer to the nearest tenth.

40 °

Use sine ratio Substitute known values Variable on top (multiply)

Solve for x using calculator

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

45𝑥

EXAMPLE: Find x using the sine ratio. Round answer to the nearest tenth.

41°

Use sine ratio Substitute known values Variable on bottom (divide)

Solve for x using a calculator

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒

40

𝑥

PRACTICE: Find x using the cosine ratio. Round answer to the nearest tenth.

65 °

Use cosine ratio

Substitute known values Variable on bottom (divide)

Solve for x using a calculator

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

𝑥17

PRACTICE: Find x using the cosine ratio. Round answer to the nearest tenth.

63 °

Use cosine ratio

Substitute known values

Variable on top (multiply)

Solve for x using calculator

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑥

52

PRACTICE: Find x using the tangent ratio. Round answer to the nearest tenth.

26 °

Use tangent ratio Substitute known values Variable on bottom (divide)

Solve for x using a calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

HOMEWORK #3:

Solving for missing sides WS

If finished, work on other assignments:

HW #1: Intro to TRIG WSHW #2: Pg. 856: 3-7, 9-14