### Exponential and Trigonometric Proof

Why is e^ik(Pi) = e-ik(Pi)?

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Why is e^ik(Pi) = e-ik(Pi)?

Please explain steps and formula. Only 12, 13, 14, 15

Can you tell me how to find the depth of the of the V in this object?

Describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. 43. y=0.5 sin 3x How do you come up with the following answer? starting from y=sinx, horizontally shrink by 1/3 and vertically shrink by 0.5 45. y= -2/3 cos x/3 How do you come up with the following answer? s

Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is 5.7 centimeters and the radius of the larger wheel is 18.1 centimeters. Through how many degrees will the larger wheel rotate if the smaller one roatates 151 degrees? ans. 47.55 deg

Write the given expression in algebraic form sin(arctan x/4)

Complete the identity (see attached) a. sin q tan q b. -2 tan 2q c. 1+cot q d. sec q + csc q Complete the identity. Sin(a+b) cos b - cos(a+b) sin b a. sin a b. sin a b-sin a b c. 2 sin b cos b(sin a - cos a) d. sin a cos b - cos a sin b Solve the triangle. Round lengths to the nearest tenth and angle meas

Graph the function f(x){sin pi/x if x is not equal to o {0 if x = 0 where -0.2<=x<=0.2. then graph f(x) where (x) varies over a smaller interval, for example, -.06<=x<=0.06. determine lim as x approaches o of sin(pi/x) if it exists. describe in a paragraph the behavior of the values of

Solve for x 1.) 2^(x-5)=3 I know the answer is: log(base 2) of 3 +5 or 5+(ln3/ln2) but I can't figure out how to get it 2.) lnx+ln(x-1)=1 Answer: (1+square root(1+4e))/2 (Don't understand how to get that) 3.) Simplify the expression tan(inverse sinx) Answer: x/(sqaure root(1-x^2)) (Don't kno

A. A tank of mass 80 metric tons is travelling at a uniform speed of 54 KM/hr on a level terrain. It then starts travelling uphill on an incline of 1 in 10 (sine slope). Calculate the extra power required from the engine in megawatts to maintain the same speed on the incline. b. When it has travelled 100m up the incline the d

1540 mm/microseconds = ___________ m/s 1 X 10^5 cm/mlliseconds = _______1050____ m/s If a sound wave travels through soft tissue at a velocity of 1.54 mm/microsecond for 2203 ms, How far has the sound wave traveled using the echo-ranging formula d=ct, where d= distance, c= velocity, t= time Using the same formula

Given that e ^ jx + e ^ -jx e ^ jx - e ^ -jx Cos x = ----------------------, Sin x = -------------------- 2 2j using only this information, prove that Cos^2 x - Sin^2 x = 1 - 2 Sin^2 x

A cable to the top of a tower makes an angle of 35 degrees with the level ground. At a point 100 yards closer to the tower the angle of elevation to the top of the tower is 59 degrees. Estimate the length of the cable. Approximate the angle between the vectors 4i-3J and 4i+3J

Oil is being piped from an offshore oil well to a refinery on land. The shoreline is considered straight, the well is 2 miles out to sea (i.e, at a right angle to the shore), the refinery is 10 miles along the coast, underwater pipe costs $360000/mile to construct, but the pipeline only costs $260000/mile on land. Given this how

Figurative Numbers & Pythagorean Theorm. See attached file for full problem description. 9) Which basic trigonometric identity is actually a statement of the Pythagorean Theorem? Justify your answer. 5) From very early on, mathematicians were interested in finding right triangles whose sides had integer length. By the Pythag

A man holds a 178 N ball in his hand, with the forearm horizontal (see the drawing). He can support the ball in this position because of the flexor muscle force M, which is applied perpendicular to the forearm. The forearm weighs 20.2 N and has a center of gravity as indicated. (a) Find the magnitude of M. (b) Find the m

Determine the phase shift of : Question 1 y = sin x Question 2 Y = sin(x -2 )

Question 1 Determine the period of y=3 sin 2x Question 2 determine the amplitude y = -2 cos x

Question 1 solve for x y=3sin x; for x =4pi Question 2 Determine the range of the following: y= -1/2 cos x

1. y=cos x; for x=4pi 2. Determine the Amplitude of: y = 3 sin x

Betty observed that the lamp post in front of her house casts a shadow of length 8 feet when the angle of inclination of the sun is 60 degrees. How tall is the lam post? (In a 30-60-90 right triangle, the side opposite 30 is one-half the length of the hypotenuse).

1) What is a discontinuity? How are discontinuities found? Which types of graphs are continuous? 3) If Bob starts off with a salary of $50,000 and earned $1000 a year for his salary, give the equation of his salary, S, for year t. Use this equation to find the year in which he would be earning $56,400. Show all your work usin

One force is pushing an object in a direction 50 degree south of east with a force of 25 Newton. A second force is simultaneously pushing the object in a direction 70 degree north of west with a force of 60 Newton. If the object is to remain stationary, give the direction and magnitude of the third force which must be applied to

Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilize the door by attaching a steel cable diagonally. If the cable measures sq 194/2 ft, what are the dimensions of the door?

Solve the system of equations: y = 3x -14 Y = 5x - 20 a. (-3,5) b. (3,5) c. Dependent d. Inconsistent Evaluate: 7 6 a. 5040 b. 42 c. 13 d. 7 See attached file for full problem description.

The hypotenuse of a right triangle is 2.7 units long. The longer leg is 1.6 units longer than the shorter leg. Find the lengths of the side of the triangle.

I need to verify this expression and I'm stuck... should I divide both sides by 2 first? Please advise as to the proper steps to take in this verification.

Give a polar equation for the curve whose graph is a vertical line that passes 3 units to the right of the origin. A parabolic reflector has a width w=20 feet and a depth d =4 feet. how far from the center will the focal point be? See attached for third question

Solve the system x-2y+z=-1 and system x+2y-2z=-1 -2x+3y+2z=4 x+3y+z=10 2x+y+3z=9 2x+6y+2z=20 Find the maximum value of c=6X + 5y on the region determined by the constaints 3x+2y+>or equal to 20 2< or equal to X<or equal to 8 1< or eq

A triangle plot of land has sides of lengths 130 feet, 110 feet, and 100 feet. Approximate the smallest angle between the sides. A radar operator sights two objects, one at a distance of 7 miles and the other at a distance of 12 miles. If the angle between the sightings is 35 degrees, how far apart are the object? A