Find the indicated function value. If it is undefined, say so. See Example 4. tan 450°

Verified step by step guidance

Convert the angle from degrees to a standard position by subtracting multiples of 360° until the angle is between 0° and 360°. For 450°, subtract 360° to get 90°.

Recognize that 90° is a special angle on the unit circle.

Recall that the tangent function, \( \tan(\theta) \), is defined as \( \frac{\sin(\theta)}{\cos(\theta)} \).

For 90°, the sine value is 1 and the cosine value is 0.

Since division by zero is undefined, \( \tan(90°) \) is undefined.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate angles to ratios of sides in right triangles. The tangent function, specifically, is defined as the ratio of the opposite side to the adjacent side. Understanding these functions is crucial for evaluating angles and their corresponding values.

Unit Circle

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It provides a geometric interpretation of trigonometric functions, where angles correspond to points on the circle. For example, the tangent of an angle can be visualized as the y-coordinate divided by the x-coordinate of the point on the unit circle.

Angle Measurement

Angles can be measured in degrees or radians, with 360 degrees equivalent to 2π radians. The angle of 450° exceeds a full rotation (360°), which means it can be simplified by subtracting 360°, resulting in an equivalent angle of 90°. This simplification is essential for evaluating trigonometric functions accurately.

Watch next

Master Introduction to Trigonometric Functions with a bite sized video explanation from Patrick

Start learning