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Pythagorean (Pythagorus) Theorem Question

A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides' measurements are 3 feet and 4 feet.

Right Triangle Trigonometry Application Word Problems : Airplane Flight Path

An airplane flies at a heading of 130° for 30 minutes and then changes to a heading of 220° and flies for 2 more hours. If the average speed of the plane is 250 miles per hour and the wind is negligible, find: a. The distance of the plane from the starting point. b. The heading the plane would have taken to get directly

Find the equation of a tangent given parametric equations

1.) Find and equation of the tangent to the curve at the point corresponding to the given value of the parameter x= cos t + sin 2t, y= sin t + cos 2t (t=0) 2.) Find dy/dx and d^2/dx^2 for which values of t is the curve concave upward x= t + ln t, y = 1 - ln t

Prove Trigonometric Identities

1. secx/csc/ + sinx/cosx = 2 tanx 2. 1+cscx/cscx = cos²x/1-sinx 3. sin2x = 2cotx/csc²x 5.tanx-tany/cotx-coty = -tanxtany 6. secxcotx=cscx

Steady-state value of voltage across a capacitor

A full-wave rectified sine voltage v(t) with an amplitude of 10 V and period 10 seconds is applied to an RLC series circuit with R = 4 ohms, L = 2H, and C = 0.2 F. Find the first six terms of the steady-state value of the voltage across the capacitor. Use MATLAB (if possible, if not, ok).

Trigonometry Application Word Problems - Fire Center

Researchers at the National Interagency Fire center in Boise , Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States . In an effort to dispatch firefighters for containment , scientists and meteologists attempts to forecast

Trigonometry Application Word Problems

A recent land survey was conducted on a vacant lot where a commercial building is to be erected . The plans for the future building construction call for a building having a roof supported by two sets of beams. The beams in the front are 8 feet high and the back beams

Trigonometry Applications to Word Problems

You have been contacting cartographers and land surveyors to explore how they utilize graphs of functions in their work , and have learned that they create formulas to calculate size and mass. Complete the following problems: 1. A lobster boat is situated due west of a lighthouse. A barge is 12 km south of the lobster boat .

Finding the height of the wall.

Elena likes to climb a vertical rock wall at an amusement park. From a point that is 10M from the base of the wall, the angle of the elevation of the top of the wall is 72 degree. What is the height of the wall, to the nearrest metre?

Few trigonometric identities are to be proved.

Prove this identity: 7. sin(x+y)/sin(x-y) = coty +cotx / coty - cot x 8. simplify: 2 sinxcos³x - 2 sin³xcosx 9. If cosx=-1/4 and pie/2<x<pie, the cos (pie/6 - x) = ? 10. Prove this identity: cos 8x = cos²4x - sin²4x

Solving for X : Trigonometric Equations (13 Problems)

Use factoring, the quadratic formula, or identities to solve the equations. Find all solutions in the interval (0,2pi) 65. 3 sin²x - 8 sin x - 3 = 0 answer x=3.4814, 5.9433 67. 2 tan²x + 5 tan x + 3 = 0 answer x= 3pi/4, 7pi/4, 2.1588, 5.3004 69. cotxcosx=cosx ans. x=pi/4, pi/2, 5pi/4, 3pi/2 71. cos x csc

Compound Angle Formula : Current, Voltage and Phase Angle

1. Alternating currents are given by: and By making use of the Compound Angle Formulae determine: a. The maximum value of the resultant current b. Its frequency c. Its Phase angle 2. The voltage and current in a circuit are given by: and By making use of Products to Sums Formulae determin

Proving Trigonometric Identities (5 Problems)

Prove the following identities..."not an identity" is an option. Please explain in detail and in steps how to perform the following: 1. cot²x-cos²x=cos²xcot²x 3. tanx= square rt of sec²x-1 4. sinx/1-cotx + cosx/1-tanx=cosx+sinx 5. cotx-1/1-tanx = cscx/secx 6. cosxsiny=1/2(sin(x+y)-sin(x-y)

Inverse Functions

Find the exact value of the expression(Consider interval is [0,pi] I) 1) sin^-1 SQRT3 / 2 = pi/3 2) arctan(-1) = 3pi / 4 3) csc^-1 2 = pi/6 4) sec^-1 SQRT(2) = pi/4 II) We were given the example to derive sin^-1x as follows. y=sin^-1 (x) siny = x (cosy)(dy/dx) = 1 (dy/dx) = 1/cosy = 1 / (SQRT(1-sin^2 (y)) = 1

Right triangle trigonometry college algebraic

A. As a group, work together to submit the answers to the following problems. Use the Small Group Discussion Board to divide tasks, discuss strategies for solving problems, and check each other's work. The finished product should be one combined document for the entire group, showing all calculations and graphical representat

Trigonometric Identities

43. Express cos 3 in terms of cos x. ans. cos3x=4cos^3x-3cosx 47. 2 cos 2y sin 2 y ans. sin 4y 51. sin 16x = 2 sin 8 x cos 8x ans. sin 16x=sin (2(8x))= 2 sin 8x cos 8x 55.cos 4x=2cos2x-1 ans. not an identity

Travel in Kilometers

Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point? Can you show me how you got the answer?