Manipulate trigonometric expressions, sketch graphs of trigonometric functions and solve equations. Find the general solution of the following trigonometric equations: 1.a)cosθcos(pi/6)+sinθsin(pi/6) =0.25 b) 2sin^2 x - 5cosx+ 1 = 0 2. Prove: cos(θ+ pi/4) - sin(θ + pi/4) = 2cos(θ+ pi/4)
1. a. square root of x-2 = 1 show work b. square root of x cubed = 27 show work c. 3 x the square root of x squared = 9 show work 2. Is the square root of x squared = x an identity (true for all non values of x?) Explain answer 3. For the equation x - 2 times square root of x on the same gr
Verify the following identities: a. cos x (tan^2 x + 1) = sec x b. 1 _________ = 1 tan x csc x c. (sin^2 x - sin^4 x)cos x = cos^3 x sin ^2 x
A boat leaves a port and sails 10 miles at a bearing of S 15° E. Another boat leaves the same port and sails 15 miles at a bearing of S 30° W. How far apart are the two boats at this point?
Lpf = ones(1,10); y=abs(fft([lpf zeros(1,246)])); Create a signal consisting of a 500 and 1000Hz cosine sampled t 10kHz. fs= 10e3; t =(0:1:0.02*fs); f1=500; f2=1000; s=cos(2*pi*t*f1/fs)+cos(2*pi*t*f2/fs); Plot the convolution of the signal with lpf, from the command filtered=conv(s,lpf) **Plot the magnitude of th
1. Find B to the nearest degree in triangle ABC given A = 34 degrees, b=7.0 and a = 11. 2. How do you convert from degrees to radians. Explain and provide an example with 283 degrees. 3. The hypotenuse of a 30-60-90 triangle is 10. Find the perimeter 4. Given C= 61 degrees, a=55, and b= 29, find the area of triang
Solve the five given problems in calculus and trigonometry. One problem entails evaluating a specified integral, another entails evaluating the cotangent function of a specified angle in radians, and each of the other four problems entails finding the Maclaurin series for either the sine function or some composite of the sine function.
Do the following problems: (1) Find the value of twice the integral of the function u^(-1) + 3*[u^(-2)] over the interval [-3, -1]. (2) Show that cot(pi/3) = 1/[sqrt(3)], where "sqrt" stands for "square root." (3) Obtain the Maclaurin series for the function f(x) = sin x. (4) Obtain the Maclaurin series for the funct
What are the antiderivatives of: COS^2 theta and SIN^2 theta and how did you find these antiderivatives.
Limit x-->0 of a trigonometric inverse function is to be found.
Parametric equations of a curve are given. The task is to Prove that tangent is parallel to x-axis and the equation to the tangent as given in the question. File attached in word format.
Consider the graph of y = tan x (see attached). (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?
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