Reciprocal Trig Functions: csc, sec, cot

Grade 10·24 problems·~35 min·ACT Math·topic·act-geo-trig-recip

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Recall / Warm-Up

In a right triangle, $\sin(\theta)$ equals which ratio?

adjacent / hypotenuse

opposite / hypotenuse

opposite / adjacent

hypotenuse / opposite

What is the value of $\cos(60\degree)$ ?

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{\sqrt{2}}{2}$

$1$

$Right triangle with angle A at bottom-left, right angle at B, sides 8, 6, and hypotenuse 10$

In the right triangle shown, which expression equals the tangent of angle A?

$\frac{6}{10}$

$\frac{8}{10}$

$\frac{6}{8}$

$\frac{8}{6}$

In a right triangle, which expression is equal to $\tan(\theta)$ ?

$\frac{\cos(\theta)}{\sin(\theta)}$

$\frac{\sin(\theta)}{\cos(\theta)}$

$\sin(\theta) \cdot \cos(\theta)$

$\frac{1}{\sin(\theta)}$

Fluency Practice

Which function is the reciprocal of $\sin(\theta)$ ?

$\sec(\theta)$

$\csc(\theta)$

$\cot(\theta)$

$\sin^{-1}(\theta)$

In a right triangle, if the side opposite angle $\theta$ is 5 and the hypotenuse is 13, what is $\csc(\theta)$ ?

$\frac{5}{13}$

$\frac{13}{5}$

$\frac{13}{12}$

$\frac{12}{5}$

What is $\csc(30\degree)$ ?

What is $\sec(30\degree)$ ? Express your answer in rationalized form.

$\frac{2\sqrt{3}}{3}$

$2\sqrt{3}$

$2$

$\frac{\sqrt{3}}{2}$

What is $\cot(60\degree)$ ? Express your answer in rationalized form.

$\sqrt{3}$

$\frac{2\sqrt{3}}{3}$

$\frac{\sqrt{3}}{3}$

$1$

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