Question

Describe and correct the error in finding csc θ, given that θ is an acute angle of a right triangle and cos θ =7/11

Answer 1

cosecθ = 1/sinθ = 11/6√2

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 = √(72) \\opp = 6√(2)`

sinθ = 6√2/11

cosecθ = 1/sinθ = 1/( 6√2/11)

cosecθ = 1/sinθ = 11/6√2

Note the error; cscθ
`\\eq` 1/cosθ but cscθ = 1/sinθ