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.
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
103. Solve the equation cos^2x +2 sin x +1 = 0 for the domain 0<x<6.28rad or 360 degree
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
Applications of Trigonometry Word Problems : Tangent Function, Nautical Miles and Polar Coordinates of Nonagon Vertices
1. Consider the graph of y = tan x. (a) How does it show that the tangent of 90 degrees is undefined? (b) What are other undefined x values? (c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)? (d) How does the graph show this? 2. A nautical mile depend
How does the graph of y=tan x show that the tangent of 90 degrees is undefined?
Prove the identities. A) TANa + 1 = 1 ------ ------------ TANa SINa COSa B) TANa-1= SIN^2a - COS^2a ------------------------ SINa COSa + COS^2a
Why can (x+450) be simplified by cosine and sin, but not tan?
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
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).
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
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
Please redo these showing all details.
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 .
Not quite sure how to work these problems
1. Find the exact value of the sine, cosine, and tangent of the angle. 11pie/12 2. Find all solutions of the equation in the interval [0, 2pie). Sin(x-5pie/6)-sin(x+ 5pie/6) =1 3. Find the exact value of sin2x using the double angle formula. Please help explain the use of the double angle formula. Sin x=1/7, 0<x<pie/2 4. Given cos theta = 4/9, where 3pie/2 <or equal to theta <or equal to 2pie. 5. Express 2sin3xcos6x as a sum containing only sines or cosines. 6. Express cos7x-cos5x as a product containing only sines and/or cosines. 7. Evaluate the expressions without the aid of a calculator. a. Arctan(- sqrt3/3) b. Arcsin(-1/2) 8. Use inverse functions to evaluate the expressions, a. cos(arcsin(sqrt5/5)) b. cos(arctan(sqrt2/x)) 9. Identify the x-values that are solutions of the equations. a. 8cos x-4 = 0 b. 18cot^2 x-18 = 0 10. A large pole is 175 feet tall. On a particular day at noon it casts a 198-foot shadow. What is the sun's angle of elevation?
1. Find the exact value of the sine, cosine, and tangent of the angle. 11pie/12 2. Find all solutions of the equation in the interval [0, 2pie). Sin(x-5pie/6)-sin(x+ 5pie/6) =1 3. Find the exact value of sin2x using the double angle formula. Please help explain the use of the double angle formula. Sin x=1/7,
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?
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
Solve: (0°<0<360°) 2sin 2x + 2 = 1
Prove : tanx + 1 / tanx = 1 / sinx cos x I'm not quite sure how I would prove this, I know it is a certain formula, but I don't not know how it applies.
Trigonometry Application Word Problems and Pythagorean Theorem : Finding the Length of the Hypotenuse of a Triangle
A radio station is going to construct a 12 foot tower for a new antenna on top of a tall building. The tower will be supported by three cables, each attached to the top of the tower and to points on the roof of the building which are 5 feet from the base of the tower. What is the total length of these three cables? 39 feet Ca
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
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
Finding the perimeter of a right triangle given hypotenuse and angles; Displacement of an oscillating bob; Completing a trigonometric identity; Trigonometric graphs
1. The hypotenuse of a 30-60-90 triangle is 9. Find the perimeter. 2. I am so lost with this one its not funny (-.6t/40) _______________ The displacement, d=-7e cos(√(pi/3)^2-0.36/1600) t) Should read: d= negative seven (e) to the negative .6t divided by 40, COS (pi divided
Please explain how to work these problems in steps 1. Prove this identity: sin(x+y)/sin(x-y) = coty+cotx/coty-cotx 8. Simplify: 2sinxcos³x-2sin³xcosx 9. If cosx=-¼and Pi/2 < x < pi, then cos (pi/6 - x) = ? 10. Prove this identity: cos8x=cos²4x-sin²4x
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)
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
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
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
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?