The diagram shows an isosceles triangle PQR inscribed in a circle, centre O, radius r cm PR QR and angle ORP radians Triangle PQR has an area of A cm 2 a Show that A r 2 sin 2 r 2 sin 2 cos 2 b Find the value of for which A has a stationary value and determine the nature of this stationary value R...

The below diagram shows angles in degrees but obviously the calculations would have to be done ...

The diagram shows an isosceles triangle PQR inscribed in a circle, centre O, radius r cm. PR

Question:

The diagram shows an isosceles triangle PQR inscribed in a circle, centre O, radius r cm.

PR = QR and angle ORP = θ radians.

Triangle PQR has an area of A cm².

a. Show that A = r² sin 2θ + r² sin 2θ cos 2θ.

b. Find the value of θ for which A has a stationary value and determine the nature of this stationary value.

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

Step by Step Answer:

Related Book For book-img-for-question

Cambridge IGCSE And O Level Additional Mathematics Coursebook

ISBN: 9781108411660

2nd Edition

Authors: Sue Pemberton

See More Books

Question Posted: Sep 02, 2021 12:51 AM

See More Questions

An equilateral triangle is inscribed in a circle of radius r. See the figure. Express the circumference C of the circle as a function of the length x of a side of the triangle. First show that r 2 =...
A rectangle is inscribed in a circle of radius 2. See the figure. Let P = (x, y) be the point in quadrant I that is a vertex of the rectangle and is on the circle. (a) Express the area A of the...
Find the value x for which: (Round your answers to 3 decimal places. You may find it useful to reference the appropriate table: chi-square table or F table) P(x216 > ) %3D 0.025x162 ) 3 b. Px216 2 X)...
Which of the environmental policy options discussed in this and previous chapters would you recommend if a hypothetical society were facing the following environmental problems? In each case, briefly...
You fill a balloon with helium gas to a volume of 2.68 L at 23oC and 789 mmHg. Now you release the balloon. What would be the volume of helium if its pressure changed to 632 mmHg but the temperature...
Stromski Company is considering a capital investment of $150,000 in additional productive facilities. The new machinery is expected to have a useful life of 5 years with no salvage value ....
What is the difference between confidence and positive confidence?
According to ightstats.com, American Airlines ights from Dallas to Chicago are on time 80% of the time. Suppose 15 ights are randomly selected, and the number of on-time ights is recorded. (a)...
Stosch Company's balance sheet reported assets of $57,000, liabilities of $18,000 and common stock of $15,000 as of December 31, Year 1. If Retained Earnings on the balance sheet as of December 31,...
A real estate developer wishes to study the relationship between the size of home a client will purchase (in square feet) and other variables. Possible independent variables include the family...
The diagram shows a semi-circle with diameter EF of length 12 cm. Angle GEF = radians and the shaded region has an area of A cm 2 . a. Show that A = 36 + 18 sin 2. b. Given that is increasing at a...
P is the point (2, 1) and Q is the point (8, 2). a. Write the equation of the straight line joining P and Q. b. Find the coordinates of M, the midpoint of PQ. c. Write the equation of the...
What policy mistakes were made in the Great Depression? How can these mistakes be shown using the 3-equation model? Show in a diagram how fiscal stimulus could have averted a deflation trap.
How have your organizations performed relative to improving healthcare quality and meeting the required standards (Medicare metrics) for value-based purchasing initiatives?
/ Precalculus Algebra Problem. 1: Consider the function f(x)=-5x5 + +-4. How many terms in f(x) are not monomials? Problem. 2: Consider the function f(x)=-3x-4x - 3x + 12. How many terms in f(x) are...
D 0
What NaCl concentration results when 279 mL of a 0.680 M NaCl solution is mixed with 462 mL of a 0.450 M NaCl solution? concentration: M
Use JavaFX's shape's classes from javafx.scene.shape package to complete the following questions (Hint: CANNOT use any Gaphics or Graphics2D classes from java.awt packages): DO not write the whole...
Merger Co. has 10 employees, each of whom earns $2,000 per month and has been employed since January 1. FICA Social Security taxes are 6.2% of the first $127,200 paid to each employee, and FICA...
The column shown in the figure is fixed at the base and free at the upper end. A compressive load P acts at the top of the column with an eccentricity e from the axis of the column. Beginning with...
Bart and Kesha, who are in the 39.6% tax bracket, are interested in reducing their taxes. They are currently considering several alternatives. For each, indicate how much tax, if any, they would...
Ken and Lynn paid $5,000 to purchase Series EE bonds in the name of their 11-year-old son. The son has no other income, and they are in the 28% tax bracket. The taxable interest this year will be...
Matt and Sandy reside in a community property state. Matt left home in April 2017 because of disputes with his wife, Sandy. Subsequently, Matt earned $15,000. Before leaving home in April, Matt...
What is the present value of $500 invested each year for 10 years at a rate of 5%?
GL1203 - Based on Problem 12-6A Golden Company LO P2, P3 Golden Corp.'s current year income statement, comparative balance sheets, and additional information follow. For the year, (1) all sales are...
A project with an initial cost of $27,950 is expected to generate cash flows of $6,800, $8,900, $9,200, $8,100, and $7,600 over each of the next five years, respectively. What is the project's...

The diagram shows an isosceles triangle PQR inscribed in a circle, centre O, radius r cm. PR

Question:

R

Step by Step Answer:

The below diagram shows angles in degrees but obviously the calculations would have to be done ...View the full answer

Cambridge IGCSE And O Level Additional Mathematics Coursebook

Students also viewed these Business questions