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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 :

Mhanifaidn

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°}
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