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sergij07 [2.7K]
3 years ago
12

If cot theta= 4/3, find csc theta

Mathematics
1 answer:
Marrrta [24]3 years ago
8 0

Answer: Option d.

Step-by-step explanation:

The trigonometric identity needed is:

csc^2\theta=cot^2\theta+1

Knowing that cot\theta=\frac{4}{3}:

Substitute it into csc^2\theta=cot^2\theta+1:

csc^2\theta=(\frac{4}{3})^2+1

Simplify the expression:

csc^2\theta=(\frac{4}{3})^2+1\\\\csc^2\theta=\frac{16}{9}+1\\\\csc^2\theta=\frac{25}{9}

Solve for csc\theta. Apply square root at both sides of the expression:

\sqrt{csc^2\theta}=\±\sqrt{\frac{25}{9}}

csc\theta=\frac{5}{3}

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