Question

θ is an acute angle and sin θ and cos θ are given. use identities to find tan θ, csc θ, sec θ, and cot θ. where necessary, rationalize denominators. sin θ = 24/25, cos θ = 7/25 tan θ = 24/7 (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. rationalize all denominators.) csc θ = □ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. rationalize all denominators.)

Explanation:

Step1: Recall the reciprocal identity for cosecant

The reciprocal identity for cosecant is \( \csc\theta=\frac{1}{\sin\theta} \).

Step2: Substitute the given value of \( \sin\theta \)

We know that \( \sin\theta = \frac{24}{25} \), so substitute this into the identity: \( \csc\theta=\frac{1}{\frac{24}{25}} \).

Step3: Simplify the fraction

Dividing by a fraction is the same as multiplying by its reciprocal, so \( \frac{1}{\frac{24}{25}} = 1\times\frac{25}{24}=\frac{25}{24} \).

Answer:

\( \frac{25}{24} \)