Textbook Question
Find each exact function value. See Example 2.
sin (-4π/3)
878
views
3. Unit Circle
Trigonometric Functions on the Unit Circle
Problem 35
Textbook Question
Find a calculator approximation to four decimal places for each circular function value. See Example 3. cos (-1.1519)
Verified step by step guidance1
Recognize that the problem asks for the value of the cosine function at the angle \(-1.1519\) radians. The cosine function is even, meaning \(\cos(-x) = \cos(x)\), so you can work with the positive angle \$1.1519$ radians if you prefer.
Recall that the cosine function gives the horizontal coordinate of a point on the unit circle corresponding to the given angle measured in radians.
Use a scientific calculator or a calculator app that supports trigonometric functions in radian mode. Make sure the calculator is set to radians, not degrees.
Input the angle \(-1.1519\) (or \$1.1519$) into the cosine function on the calculator: calculate \(\cos(-1.1519)\).
Round the result to four decimal places to get the final approximation.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Circular Functions and the Unit Circle
Circular functions like cosine are defined using the unit circle, where the angle corresponds to a point on the circle. The cosine of an angle is the x-coordinate of that point, allowing us to interpret cosine values geometrically for any real angle, including negative angles.
Recommended video:
06:11
Introduction to the Unit Circle
Evaluating Trigonometric Functions for Negative Angles
Negative angles represent clockwise rotation from the positive x-axis. The cosine function is even, meaning cos(-θ) = cos(θ), so the cosine value for a negative angle equals that of its positive counterpart, simplifying calculations and understanding.
Recommended video:
7:28Evaluate Composite Functions - Values Not on Unit Circle
Using Calculators for Trigonometric Approximations
Calculators can approximate trigonometric values to a desired decimal precision. Ensure the calculator is set to the correct mode (radians or degrees) matching the angle's unit, then compute the cosine and round the result to four decimal places as required.
Recommended video:
4:45How to Use a Calculator for Trig Functions
Related Videos
Related Practice