Question

Assume that $\alpha$ is an angle in standard position whose terminal side. contains the given point and that $0^{\circ}<\alpha<90^{\circ}$. Find the degree measure of $\alpha$ to the nearest tenth of a degree. $$(1.5,9)$$

Name: Problem 19, Chapter 5: Precalculus Functions and Graphs
Uploaded: 2020-05-22T23:21:13-08:00
Duration: 2 min 26 s
Channel: Melissa Salvador
Description: Assume that αis an angle in standard position whose terminal side. contains the given point and that 0^∘<α<90^∘. Find the degree measure of αto the nearest tenth of a degree. (1.5,9)

   Assume that $\alpha$ is an angle in standard position whose terminal side.
contains the given point and that $0^{\circ}<\alpha<90^{\circ}$. Find the degree measure of $\alpha$ to the nearest tenth of a degree.
$$(1.5,9)$$

Precalculus Functions and Graphs

Mark Dugopolski 4th Edition

Chapter 5, Problem 19

Instant Answer

Solved by Expert Melissa Salvador

05/22/2020

Step 1

5, 9) which lies on the terminal side of the angle $\alpha$. We can form a right triangle with the x-axis and the line segment from the origin to the point (1.5, 9). The horizontal side of the triangle (adjacent to $\alpha$) is 1.5 units long and the vertical side Show more…

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Assume that $\alpha$ is an angle in standard position whose terminal side. contains the given point and that $0^{\circ}<\alpha<90^{\circ}$. Find the degree measure of $\alpha$ to the nearest tenth of a degree. $$(1.5,9)$$

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Key Concepts

Standard Position

An angle in standard position has its vertex at the origin and its initial side along the positive x-axis. This setup is essential in relating the coordinates of a point on the terminal side of the angle to the corresponding trigonometric functions.

Tangent Function and Its Inverse

The tangent of an angle is defined as the ratio of the y-coordinate to the x-coordinate of a point on its terminal side. In cases where the angle is restricted to the first quadrant, using the inverse tangent function (arctan) allows one to compute the angle whose tangent is a given value.

Using Coordinates to Determine Trigonometric Ratios

When a point lies on the terminal side of an angle in the coordinate plane, its x and y coordinates can be used to calculate trigonometric ratios such as sine, cosine, and tangent. This method is fundamental in solving problems that involve finding the measure of an angle given specific coordinate values.

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