To determine The all values of θ between 0 and 2 π that satisfies the equation cos θ = 1 2 . Explanation Property used: Properties of a right triangle: Triangle with 30 ° − 60 ° − 90 ° : “In a right triangle having angles of 30 ° , 60 ° , and 90 ° the hypotenuse is always twice as long as the shortest side, and the middle side has a length that is 3 times as long as that of the shortest side. Also, the shortest side is opposite the 30 ° angle. Triangle with 45 ° − 45 ° − 90 ° : In a right triangle having angles of 45 ° , 45 ° , and 90 ° the hypotenuse has a length that is 2 times as long as the length of either of the shorter (equal ) sides.” Formula used: “Let ( x , y ) be a point other than the origin on the terminal side of an angle θ in standard position. Let r be the distance from the origin to ( x , y ) . Then sin θ = y r , cos θ = x r , tan θ = y x , cot θ = x y , sec θ = r x and csc θ = r y ”. Pythagorean theorem: In a triangle with a right angle, if the longest side of the triangle c and the shorter sides are a and b , then c 2 = a 2 + b 2 . Here, longest side of the triangle is r and shorter sides are x and y . Calculation: Consider the equation cos θ = 1 2 . By the above formula, cos θ can be defined as cos θ = x r . That is, x = 1 and r = 2 . In order to find the all values of θ between 0 and 2 π , first find the value of y

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 13.1, Problem 49E

To determine

The all values of θ between 0 and 2π that satisfies the equation cosθ=12.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.1, Problem 48E

Chapter 13.1, Problem 50E

Students have asked these similar questions

Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)

There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three investment? STEP 1: The formula for compound interest is A = nt = P(1 + − − ) n², where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to A = Pert Find r and n for each model, and use these values to write A in terms of t for each case. Annual Model r=0.10 A = Y(t) = 1150 (1.10)* n = 1 Quarterly Model r = 0.10 n = 4 A = Q(t) = 1150(1.025) 4t Continuous Model r=0.10 A = C(t) =…

Chapter 13 Solutions

Calculus with Applications (11th Edition)

Ch. 13.1 - (a) Convert 210° to radians. (b) Convert 3π/4...Ch. 13.1 - Find the values of the six trigonometric functions...Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Find all values of θ between 0 and 2π that satisfy...Ch. 13.1 - Convert the following degree measures to radians....Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Convert the following degree measures to radians....Ch. 13.1 - Prob. 5E

Knowledge Booster

$Calculus$

Learn more about

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