a Show that 18 is a root of the equation sin3 cos 2 b Express sin3 and cos 2 in terms of sin c Hence show that sin18 is a root of the equation 4x 3 2x 2 3x 1 0 d Hence find the exact value of sin18 ...

a To show that 18 is a root of the equation sin3 cos 2 we can substitute 18 or 10 in radians and che ...

a. Show that = 18 is a root of the equation sin3 = cos 2. b.

Question:

a. Show that θ = 18° is a root of the equation sin3θ = cos 2θ.

b. Express sin3θ and cos 2θ in terms of sinθ.

c. Hence show that sin18° is a root of the equation 4x³ − 2x² − 3x + 1 = 0.

d. Hence find the exact value of sin18°.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

ISBN: 9781108407199

1st Edition

Authors: Sue Pemberton, Julianne Hughes, Julian Gilbey

See More Books

Question Posted: Mar 14, 2023 07:16 AM

See More Questions

Find the positive root of the equation (4 - 2) x 2 - (1 + 22) x - 1 = 0. Write your answer in the form a+b2/c, where a, b and c are integers.
Find the real root of the equation 1.02x^2 + x - 1 = 0 that lies between 0.7 and 0.8 to 3 decimal places, using the simple iteration method. (9 Marks)
Show that there is a root of the equation below between 1 and 2. 4x36x2 + 3x-2=0 SOLUTION Let f(x) = 4x - 6x + 3x - 2. We are looking for a solution of the given equation, that is, a number c between...
Chee, single, age 40, had the following income and expenses during 2017: Calculate Chees taxable income for the year before personal exemptions. If Chee has any options, choose the method that...
Go to www.mcdonalds.com and analyze McDonalds positioning initiatives and discuss important positioning issues for McDonalds.
What obvious question arises when we examine historical patterns in aggregate dividend payouts?
Show that if $\mu_{i j}=\mu+\alpha_{i}+\beta_{j}$, the mean of the $\mu_{i j}$ (summed on $j$ ) is equal to $\mu+\alpha_{i}$, and the mean of $\mu_{i j}$ (summed on $i$ and $j$ ) is...
The accompanying flowchart on page 330 summarizes Jenz Corporations processing of sales. Some of the flowchart symbols are labeled to indicate controls and records. For each symbol numbered 1 through...
RESUME PROJECT: Develop a detailed job description for Patient Care Associate/ Patient care technician. Compare this description to your current resume. What similarities and differences do you...
a. Find the maximum and minimum values of 7 sin 2 + 9 cos 2 + 4sin cos + 2. b. Hence, or otherwise, solve the equation 7 sin 2 + 9 cos 2 + 4sin cos = 10 for 0 < < 360.
It is given that 2 ln(4x 5) + ln(x + 1) = 3ln3. i. Show that 16x3 24x 2 15x 2 = 0. ii. By first using the factor theorem, factorise 16x 3 24x 2 15x 2 completely. iii. Hence solve the equation...
During the month of May, Russnak Corporation, a manufacturing company, purchased raw materials costing $73,000. The cost of goods manufactured for the month was $102,000. The beginning balance in the...
1. For the following program segment, give the output produced by the segment: 1 int i = 13; 2 while (i> 0) { int j = 2; while (j
Killer Whale, Inc. has the following balance sheet statement items: total current liabilities of $681,770; net fixed and other assets of $1,284,265; total assets of $3,395,673; and long-term debt of...
Question 5 The following information pertains to Questions 5 - 6. Consider the design of a single stub matching network (MN) for Z = (40+ j 30) 2 and Z = 50 2. Assume a shunt short-circuited stub....
DDC and Bank are finalizing the terms of a $200MM Unsecured Term Loan (UTL) with an interest rate of 5%.As part of the loan, DDC agrees it wil payoff the $50MM venture loan it previously...
the walden manufacturing corporation has office support salaries of $4000, factory supplies of $1000, indirect labor of $6000, direct materials of $16000, advertising expense of $2500, office expense...
What potential problems or challenges do you see for the consultants and the client?
Consider the discrete group G of order 8 that has the following Cayley diagram e If we have the sequence of operations: fcagec, which of the options represents the reduction of the sequence to a...
The discrete random variable Y is such that Y {4, 5, 8,14,17} and P(Y = y) is directly proportional to 1/y + 1. Find P(Y > 4).
A sewing basket contains eight reels of cotton: four are green, three are red and one is yellow. Three reels of cotton are randomly selected from the basket. a. Show that the expected number of...
A fair 4-sided die, numbered 1, 2, 3 and 5, is rolled twice. The random variable X is the sum of the two numbers on which the die comes to rest. a. Show that P(X = 8) = 1/8. b. Draw up the...
In java Implement a STACK of floats using as a linked list and as an array. You should ask the user what operation to do (Push/Pop/Peek/Clear/etc) and if needed the parameter needed then perform that...
Write a program that reads a number nuggets , (input by the user), and then calculates how many calories and displays the result. Use a named constant CALORIES_PER_NUGGET . The value to use is: 59.3...
Java program using ArrayList to allow the professor to enter students' names, and four test scores for each student. There should be an option to type "C" when student data entry is complete. Next,...

a. Show that = 18 is a root of the equation sin3 = cos 2. b.

Question:

Step by Step Answer:

a To show that 18 is a root of the equation sin3 cos 2 we can substitute 18 or 10 in radians and che...View the full answer

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

Students also viewed these Mathematics questions