In a given circle a central angle of 40° intercepts a chord of 6 cm. What is the circumference of the circle?
A long strip of insulating tape is to be wrapped around a hot water pipe. If the width of the strip is w and the diameter of the pipe is d, at what angle must the strip be placed at the edge of the pipe so that no overlapping and no spaces occur?
Given that cos 30° = √3/2 and cos 36° = (1 + √5)/4. Use formulas for the cosines of sums of angles, differences of angles, etc., to come up with an exact expression (involving radicals) for cos 3°.
Find a formula for sin A in terms of b and c only. (Note: △ABC is an isosceles triangle.)
cos21° + cos22° + cos23° + . . . + cos289° + cos290° = ?
Let tan x = (2ab)/(a2 – b2), where a > b > 0 and 0 < x < 90. Draw a right triangle with angle x and label two sides of the triangle to show tan x. Now find an expression for sin x.
A circle centered at A of radius r is externally tangent to a circle centered at B of radius 2r. Tangent lines are drawn from A to the larger circle with points of tangency at D and E respectively. Find the area of the shaded portion of the diagram.
It so happens that the triangle whose sides are 4, 5, and 6 has a special property: Its largest angle is twice its smallest angle. Make calculations that support this assertion.