Solve and state the correct answer for the trigonometric equation below tan y = 6 - 4 cot y where 0 \leqslant y \leqslant 360 ​

Question

Solve and state the correct answer for the trigonometric equation below

tan y = 6 - 4 cot y where

`0 \leqslant y \leqslant 360`
​

Answer 1

• y = {37.4°, 79.2°, 217.4°, 259.2°}

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°}