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Chapter 6: Q. 6 (page 395)

The domain of the tangent function is _____.

Short Answer

Expert verified

The domain of the tangent function is the set of all real numbers, except the odd integer multiples of $\frac{π}{2}$ .

Step by step solution

01

Step 1. Given information.

We have:

The domain of the tangent function is _____.

02

Step 2. Fill the blank.

The tangent function, the x-coordinate of $P = (x, y)$ can not be $0$ since this results in division by $0 .$

On the unit circle, there are two points $(0, 1), (0, - 1)$ . These two points correspond to the angles $\frac{π}{2}$ and $\frac{3 π}{2}$ .

Such angles must therefore be excluded from the domain of the tangent function.

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Most popular questions from this chapter

For a circle of radius r, a central angle of u degrees subtends an arc whose length s is $s = \frac{π}{180} r θ$ . Discuss whether this is a true or false statement. Give reasons to defend your position.

A function for which $f (x) = f (- x)$ for all $x$ in the domain of $f$ is called a(n) ___ function.

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(- \frac{\sqrt{5}}{3}, - \frac{2}{3})$ .

Convert each angle in degrees to radians. Express your answer as a multiple of $π$ .

$- 90 °$

The range of the sine function is _____.

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