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Rudik [331]
3 years ago
12

Trigonometry Trigonometric Functions Given: Cos θ = (3/5), Find: Csc θ

Mathematics
1 answer:
torisob [31]3 years ago
5 0

The value of \csc \theta is \frac{5}{4}

Explanation:

Given that the function cos \ \theta is cos \ \theta= \frac{3}{5}

We need to determine the value of \csc \theta

<u>The value of Opposite side of the triangle:</u>

The formula for cos \ \theta is given by

cos \ \theta= \frac{adj}{hyp}=\frac{3}{5}

The value of opposite side can be determined using the formula,

opp=\sqrt{hyp^2-adj^2

opp=\sqrt{5^2-3^2}

opp=\sqrt{25-9}

opp=\sqrt{16}=4

Thus, the value of opposite side is 4

<u>The value of </u>sin \ \theta<u>:</u>

The formula for sin \ \theta is given by

sin \ \theta= \frac{opp}{hyp}

Substituting the values, we have,

sin \ \theta= \frac{4}{5}

Thus, the value of sin \ \theta is \frac{4}{5}

<u>The value of </u>\csc \theta<u>:</u>

The formula for \csc \theta is given by

csc \ \theta=\frac{1}{sin \ \theta}

Substituting the values, we have,

csc \ \theta=\frac{1}{\frac{4}{5}}

csc\ \theta= \frac{5}{4}

Thus, the value of \csc \theta is \frac{5}{4}

Hence, the value of \csc \theta is \frac{5}{4}

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