Homework help with ellipse and parabolas

Problems attached. Can you reccomend a graphing utility that might help as well please.

Quotient Identity and Pythagorean identity.

Prove each identity. A) TANa + 1 = 1 ------ ------------ TANa SINa COSa B) TANa-1= SIN^2a - COS^2a ------------------------ SINa COSa + COS^2a Please explane how to answear this question and show me step by step.

Problem Set

1. Find the length L from point A to the top of the pole. 2. Lookout station A is 15 km west of station B. The bearing from A to a fire directly south of B is S 37°50' E. How far is the fire from B? 3. The wheels of a car have a 24-in. diameter. When the car is being driven so that the wheels make 10 revolutions per second, how far with the car travel in one minute? 4. A regular octagon is inscribed in a circle of radius 15.8 cm. Find the perimeter of the octagon. 5. What is the angle of elevation of the sun when a 35-ft mast casts a 20-ft shadow? 6. A V-gauge is used to find the diameters of pipes. In the figure on p. 373 in the text, the measure of angle AVB is 54°. A p... click for more

Problem Set

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 depends on latitude. It is defined as length of a minute of arc of the earth's radius. The formula is N(P) = 6066 - 31 cos 2P, where P is the latitude in degrees. (a) Using the Cybrary and other course resources, find the exact latitude (to 4 decimal places) of where you live, used to live, work, or used to work (include the zip code). (b) Using the latitude found in part a a... click for more

Trig Homework

(See attached file for full problem description) --- 1. Determine the vertices and foci of the graph of x^2 y^2 ---- - ---- = 1. 16 35 As an example. Answer should look like (0, +-4/9) Vertices (+-2sqrt13, 0) Foci 2. Rotate the axes to eliminate the xy-term. 8x^2+64xy+8y^2+12x+12y+9=0 I tried to work through this one and got it this far using the formulas but am stuck in eliminating the xy. 3. Find the discriminate and classify the graph. 7x^2-9xy+4y^2-4x-4y=0 4. Find the polar form of the equation 6x^2+3xy+6y^2=(-3) 5. A soccer ball is kicked with an initial velocity of 48ft/sec at an angle of 49 dgrees to the horiz... click for more