3.09B - Finding Rule of Tangent

University:
High School
Course:
High School Physics
Academic year:

2024
Views:

437

Pages:

6
Author:

1 1

Trigonometry Lessons 3.09B Finding Rule of Tangent Functions Connect Properties Find the Rule: Steps 1. Find 𝑏 using the period 2. Find ℎ 𝑃 =distance between asymptotes 𝜋 𝜋 ⟺ 𝑏 = 𝑏 𝑃 - x-coordinate of the midpoint of the cycle - midpoint of two consecutive asymptotes 3. Find 𝑎 and 𝑘 using systems of equations 𝑓 𝑥 = 𝑎 tan 𝑏 𝑥 − ℎ +𝑘 Find the rule of the tangent function that passes through 𝜋 𝜋 , 0 and , 1 between two consecutive asymptotes 4 2 defined by equations 𝑥 = 1. 𝜋 8 and 𝑥 = 5𝜋 8 Find 𝑏 by analyzing the period 𝑃 =distance between asymptotes 5𝜋 𝜋 𝜋 = − = 8 8 2 𝜋 𝑏= 𝜋 =2 2 Find the rule of the tangent function that passes through 𝜋 𝜋 , 0 and , 1 between two consecutive asymptotes 4 2 defined by equations 𝑥 = 2. 𝜋 8 and 𝑥 = 5𝜋 8 Find ℎ -horizontal value of the “MIDPOINT OF A CYCLE” -halfway between two consecutive asymptotes 5𝜋 𝜋 + 3𝜋 8 8 = 2 8 3𝜋 𝑓 𝑥 = 𝑎 tan 2 𝑥 − 8 +𝑘 Find the rule of the tangent function that passes through 𝜋 𝜋 , 0 and , 1 between two consecutive asymptotes 4 2 defined by equations 𝑥 = 3. 𝜋 8 and 𝑥 = 5𝜋 8 Find 𝑎 and 𝑘 using systems of equations 𝜋 ,0 4 𝜋 3𝜋 0 = 𝑎 tan 2 − 4 8 𝜋 0 = 𝑎 tan − +𝑘 4 0 = 𝑎 −1 + 𝑘 +𝑘 𝜋 ,1 2 𝜋 3𝜋 1 = 𝑎 tan 2 − 2 8 1 = 𝑎 tan 1 =𝑎=𝑘 2 +𝑘 𝜋 +𝑘 4 1=𝑎 1 +𝑘 1=𝑎+𝑘 0 = −𝑎 + 𝑘 𝑎=𝑘 1=𝑎+𝑎 1 = 2𝑎 𝑓 𝑥 = 1 3𝜋 tan 2 𝑥 − 2 8 + 1 2 HW Visions 2 P110: #8