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
¿ 4
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
¿
¿
¿
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
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