Answer:
<h2>
cosecθ = 1/sinθ = 11/6√2</h2>
Step-by-step explanation:
Given that cos θ =7/11, cosec θ = 1/sinθ in trigonometry.
Based on SOH, CAH, TOA;
cosθ = adjacent/hypotenuse = 7/11
adjacent = 7 and hyp = 11
Since sinθ = opp/hyp, we need to get the opposite to be able to calculate sinθ.
Using pythagoras theorem to get the opposite;
![hyp^{2} = adj^{2} + opp ^{2} \\opp = \sqrt{hyp^{2} - adj^{2} } \\opp = \sqrt{11^{2} - 7^{2}} \\opp = \sqrt{72} \\opp = 6\sqrt{2}](https://tex.z-dn.net/?f=hyp%5E%7B2%7D%20%3D%20adj%5E%7B2%7D%20%20%2B%20opp%20%5E%7B2%7D%20%20%5C%5Copp%20%3D%20%5Csqrt%7Bhyp%5E%7B2%7D%20-%20adj%5E%7B2%7D%20%20%7D%20%5C%5Copp%20%3D%20%5Csqrt%7B11%5E%7B2%7D%20-%207%5E%7B2%7D%7D%20%5C%5Copp%20%3D%20%5Csqrt%7B72%7D%20%5C%5Copp%20%3D%206%5Csqrt%7B2%7D)
sinθ = 6√2/11
cosecθ = 1/sinθ = 1/( 6√2/11)
cosecθ = 1/sinθ = 11/6√2
Note the error; cscθ
1/cosθ but cscθ = 1/sinθ