Understanding Secant, Cosecant, and Cotangent

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Math › Understanding Secant, Cosecant, and Cotangent

Questions 1 - 2

1

Which of these is equal to $\frac{\text{hypotenuse}}{\text{adjacent}}$ for angle ?

$\sec{x}$

$\csc{x}$

$\sin x$

$\cot{x}$

$\cos{x}$

Explanation

$\sec{x}=\frac{\text{hypotenuse}}{\text{adjacent}}$ , as it is the inverse of the $\cos{x}$ function. This is therefore the answer.

2

An angle has a cosine of $\frac{4}{5}$ . What will its cosecant be?

$\frac{5}{3}$

$\frac{5}{4}$

$\frac{3}{5}$

$\frac{3}{4}$

$\frac{4}{3}$

Explanation

The problem tells us that the cosine of the angle will be $\frac{4}{5}$ . Cosine is the adjacent over the hypotenuse. From here we can use the Pythaogrean theorem:

$\text{Opposite}^2+\text{Adjacent}^2=\text{Hypotenuse}^2$

$\sqrt{O^2}=\sqrt{9}$

Now we know our opposite, adjacent, and hypotenuse.

The cosecant is $\csc=\frac{\text{Hypotenuse}}{\text{Opposite}}$ .

From here we can plug in our given values.

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

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