Explanation Definition used: 1. Let x be the radian measure of an angle in standard position, and let P = ( a , b ) be the point on the unit circle that lies on the terminal side of the angle in Figure 1. Then sin x = b and cos x = a . 2. The trigonometric function tan x = sin x cos x ; where cos x ≠ 0 . Calculation: The value of the given expression tan ( 150 ° ) is evaluated as follows. By the above definition, the expression can be rewritten as tan ( 150 ° ) = sin ( 150 ° ) cos ( 150 ° ) . The terminal side of an angle of degree measure 150 passes through the point A ( − 3 2 , 1 2 ) on the unit circle as shown below in Figure 2. From Figure 2, the x -coordinate of the point A is cos ( 150 ° ) = − 3 2 and the y -coordinate of the point A is sin ( 150 ° ) = 1 2

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

See similar textbooks

Concept explainers

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosi…

Videos

Question

Chapter 8.2, Problem 39E

To determine

To find: The exact value of tan(150°) without the use of a calculator.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 38E

Chapter 8.2, Problem 40E

Students have asked these similar questions

13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of the following sets and the cardinal number of each set. a) W° and n(W) b) (VUW) and n((V U W)') c) VUWUX and n(V U W UX) d) vnWnX and n(V WnX)

9) Use the Venn Diagram given below to determine the number elements in each of the following sets. a) n(A). b) n(A° UBC). U B oh a k gy ท W z r e t ་ C

10) Find n(K) given that n(T) = 7,n(KT) = 5,n(KUT) = 13.

Chapter 8 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 8.1 - Find the degree measure of 1 rad.Ch. 8.1 - Without using a calculator, find: (A)cot 45 (B)cos...Ch. 8.1 - Solve the right triangle in Figure 14. Round side...Ch. 8.1 - Solve the right triangle in Figure 16. Round...Ch. 8.1 - Repeat Example 5 assuming that the man is standing...Ch. 8.1 - Prob. 1ED Ch. 8.1 - Prob. 1E Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The exact value of tan ( 150 ° ) without the use of a calculator.

Solution Summary: The author explains how to find the exact value of mathrmtan(150°) without the use of a calculator.

Concept explainers

Videos

To find: The exact value of tan(150°) without the use of a calculator.

Want to see the full answer?

Chapter 8 Solutions