Textbook Question
In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
tan 32.7°
1
views
Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
Not the one you use?Change textbookSelect a different textbook
Table of contents
Chapter 1, Problem 39
In Exercises 35–60, find the reference angle for each angle.
355°
Verified step by step guidance1
Identify the quadrant in which the angle 355° lies. Since 355° is between 270° and 360°, it is in the fourth quadrant.
Recall that the reference angle is the acute angle formed between the terminal side of the given angle and the x-axis.
For angles in the fourth quadrant, the reference angle \( \theta_{ref} \) is calculated by subtracting the angle from 360°: \( \theta_{ref} = 360^\circ - \theta \).
Substitute the given angle into the formula: \( \theta_{ref} = 360^\circ - 355^\circ \).
Simplify the expression to find the reference angle.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Reference Angle
A reference angle is the acute angle formed between the terminal side of a given angle and the x-axis. It is always positive and less than or equal to 90°, used to simplify trigonometric calculations by relating any angle to an acute angle.
Recommended video:
5:31
Reference Angles on the Unit Circle
Standard Position of an Angle
An angle in standard position has its vertex at the origin and its initial side along the positive x-axis. The terminal side rotates counterclockwise for positive angles and clockwise for negative angles, determining the angle's quadrant and reference angle.
Recommended video:
05:50Drawing Angles in Standard Position
Quadrants and Angle Measurement
The coordinate plane is divided into four quadrants, each spanning 90°. Knowing the quadrant of an angle helps find its reference angle by subtracting or adding the angle to the nearest x-axis boundary (0°, 90°, 180°, 270°, or 360°).
Recommended video:
6:36Quadratic Formula
Related Practice
Textbook Question
In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.
tan θ > 0 and sec θ > 0
1
views
Textbook Question
In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places.
-4.8 radians
Textbook Question
In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
sin 38°
1
views
Textbook Question
In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places.
-5.2 radians
Textbook Question
In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.
tan θ > 0 and cos θ < 0
2
views