Answer:
1. Cos θ = 6√2 / 11
2. Tan θ = 7 / 6√2
3. Cosec θ = 11 / 7
4. Sec θ = 11 / 6√2
5. Cot θ = 6√2 / 7
Explanation:
From the question given above, the following data were obtained:
Sine θ = 7 / 11
Next, we shall determine the adjacent of the right triangle. This can be obtained as follow:
Sine θ = 7 / 11
Sine θ = Opposite / Hypothenus
Opp = 7
Hypo = 11
Adj =?
Hypo² = Opp² + Adj²
11² = 7² + Adj²
121 = 49 + Adj²
Collect like terms
Adj² = 121 – 49
Adj² = 72
Take the square root of both side
Adj = √72
Adjacent = 6√2
1. Determination of Cos θ
Adjacent = 6√2
Hypothenus = 11
Cos θ =?
Cos θ = Adjacent / Hypothenus
Cos θ = 6√2 / 11
2. Determination of Tan θ
Opposite = 7
Adjacent = 6√2
Tan θ =?
Tan θ = Opposite / Adjacent
Tan θ = 7 / 6√2
3. Determination of Cosec θ
Sine θ = 7 / 11
Cosec θ =?
Cosec θ = 1 ÷ Sine θ
Cosec θ = 1 ÷ 7 / 11
Cosec θ = 1 × 11/7
Cosec θ = 11/7
4. Determination of Sec θ
Cos θ = 6√2 / 11
Sec θ =?
Sec θ = 1 ÷ Cos θ
Sec θ = 1 ÷ 6√2 / 11
Sec θ = 1 × 11 / 6√2
Sec θ = 11 / 6√2
5. Determination of Cot θ
Tan θ = 7 / 6√2
Cot θ =?
Cot θ = 1 ÷ Tan θ
Cot θ = 1 ÷ 7 / 6√2
Cot θ = 1 × 6√2 / 7
Cot θ = 6√2 / 7