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The Pythagorean Theorem can also be proved directly, by choosing 0 at the right angle of a right-angled triangle whose other two vertices are u and v.
The sides of a square are lengthened by 6 cm, the area become 121 cm^2. Find the length of a side of the original square.
An airplane flies 180 kilometers from an airport in a direction of 260 degrees. How far west of the airport is the airplane? How far south?
Assume that the terminal side of an angle of t radians passes through the point (.9, -.4) . Find sin (t), cos (t), tan (t).
Simplify the given expression. Compute the exact answer as a fraction, it should not contain sin, cos, or tan.
Two stations are 190 miles apart, station A directly south of station B. Both spot a fire. The bearing of the fire from station A.
An airplane flies over an observer with a velocity of 400 mph and at an altitude of 2640 ft.
If in a triangle the square on one of the sides be equal to the squares on the remaining two sides of the triangle.
The number of hours of daylight in city A is given by the following equation, where x is the number of days after January 1.
How far Michelle is from the buoy, how high was the rescue team and how long was the rope that they had to throw to Sean?
Find the value of each of the following under the given conditions: tan alpha = -4/3, alpha lies in quadrant 2; cos beta = 5/6, beta lies in quadrant 1
When the baby pulls and releases the toy, it begins to bob up and down so that the distance between the toy and the bar oscillates in a sinusodial fashion.
The voltage (V) in a certain electric circuit as a function of the time (t) in seconds is given by 3.0 sin184t cos184t.
A ship captain at sea uses a sextant to sight an angle of elevation of 37 degrees to the top of lighthouse.
If t=0 represents the 6 o' clock position, find a formula to represent the height of a person on the ferris wheel after t seconds.
State the equation of the SINE function that relates the height of the horse, h, as a function of time, t.
The graph shows the variation of the water level relative to mean sea level in Commencement Bay at Tacoma, Washington, for a particular 24-hour period.
If sin(t) = -8/17 and the terminal point for t is in quadrant 4, find csc(t) + sec(t). If sec(t) = -5 and the terminal point for t is in quadrant 2, find sin^2.
In the interval 0 degrees < (or equal to) x < (or equal to) 360 degrees, how many values of x satisfy the equation 3sin (squared) (x) + sin(x) - 2 = 0?
Convert the equation to polar coordinates and simplify. Express the equation in rectangular coordinates.
Use an addition of subtraction formula to simplify the equation. Then find all solutions in the interval [0, 2*pie).
Find the exact value of the following expressions given that sec(x) = 3/2, csc(y) = 3 and x and y are in quadrant I.
The first option, Truck A, offers a flat fee of $25 and $.40 per mile. Truck B offers a flat fee of $30 and $.25 per mile.
Three circles of radii 3, 4, and 5 touch each other externally. Find the angles of the triangle formed by joining their centers.
A satellite circles the earth in such a manner that it is y miles from the equator (north or south, height from the surface not considered).