symxx
Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Solve and state the correct answer for the trigonometric equation below

tan y = 6 - 4 cot y where
[tex] 0 \leqslant y \leqslant 360[/tex]
​

Sagot :

mhanifa

Answer:

  • y = {37.4°, 79.2°, 217.4°, 259.2°}

Step-by-step explanation:

Given

  • tan y = 6 - 4 cot y

We now that

  • cot y = 1/tan y

Substitute tan y with x:

  • x = 6 - 4/x
  • x² = 6x - 4
  • x² - 6x + 4 = 0
  • x² - 6x + 9 = 5
  • (x - 3)² = 5
  • x - 3 = ± √5
  • x = 3 + √5
  • x = 3 - √5

Replace x with tan y:

  • tan y = 3 + √5 ⇒ y = arctan (3 + √5) ≈ 79.2° + 180°k
  • tan y = 3 - √5 ⇒ y = arctan (3 - √5) ≈ 37.4°  + 180°k

Answer is:

  • y = {37.4°, 79.2°, 217.4°, 259.2°}
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.