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Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given. (In image below)


Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)


Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)

Students Were Asked To Simplify The Expression The Quantity Cosecant Theta Minus Sine Theta End Quantity Over Cosecant Period Two Students Work Is Given In Imag class=

Sagot :

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Answer:

  A.  student A is correct; student B was confused by the division

  B.  3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)

Step-by-step explanation:

Each student correctly made use of the trig identities ...

  csc(θ) = 1/sin(θ)

  1 -sin²(θ) = cos²(θ)

__

A.

Student A's work is correct.

Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.

__

B.

The transition from Step 2 can look like ...

  [tex]\textsf{Step 3: }\ \dfrac{\left(\dfrac{1-\sin^2\theta}{\sin\theta}\right)}{\csc\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}\cdot\dfrac{1}{\csc\theta}=\dfrac{\cos^2\theta}{(\sin\theta)(\csc\theta)}\\\\\textsf{Step 4: }\ \cos^2\theta[/tex]

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