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Pachacha [2.7K]
2 years ago
10

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

Mathematics
1 answer:
a_sh-v [17]2 years ago
6 0

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}

sinθ = 6√2/11

cosecθ = 1/sinθ = 1/( 6√2/11)

cosecθ = 1/sinθ = 11/6√2

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

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