MA141 Grantham University Week 6 Trigonometric Equations Paper

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oqe513

Mathematics

MA141

Grantham University

Description

I need help with these questions.

  • Convert angles from degrees to radians.
  • Identify co-terminal angles.
  • Evaluate the six Trigonometric functions using a right triangle.
  • Solve trigonometric equations.

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Write a short essay explaining to a classmate how to evaluate the six trigonometric functions of any angle θ in standard position. Include in your essay an explanation of reference angles and how to use them, the signs of the functions in each of the four quadrants, and the trigonometric values of common angles. Include figures or diagrams in your essay. Week Six – Application Assignment Answer the following questions in a Word document and upload the document to the appropriate drop box. 1) The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, 2 inches, and 14 inches, respectively. A cyclist pedals at a rate of 1 revolution per second. a) Find the speed of the bicycle in feet per second and miles per hour. b) Use your result from part (a) to write a function for the distance d (in miles) a cyclist travels in terms of the number n of revolutions of the pedal sprocket. c) Write a function for the distance d (in miles) a cyclist travels in terms of the time t (in seconds). Compare this function with the function from part (b). 2) A car’s rear windshield wiper rotates 125°. The total length of the wiper mechanism is 20 inches and the length of the wiper blade is 12 inches. Find the area wiped by the wiper blade 3) A six-foot person walks from the base of a broadcasting tower directly toward the tip of the shadow cast by the tower. When the person is 132 feet from the tower and 3 feet from the tip of the shadow, the person’s shadow starts to appear beyond the tower’s shadow. a) Draw a right triangle that gives a visual representation of the problem. Label the known quantities of the triangle and use a variable to represent the height of the tower. b) Use a trigonometric function to write an equation involving the unknown quantity. c) What is the height of the tower? 4) An airplane, flying at an altitude of 6 miles, is on a flight path that passes directly over an observer. Let θ be the angle of elevation from the observer to the plane. Find the distance d from the observer to the plane when: a) θ = 30° b) θ = 90°, c) θ = 120° 5) A baseball is hit at an angle θ horizontal with the ground. Suppose the initial velocity is 100 feet per second. An outfielder catches the ball 300 feet from home plate. Find the angle given the range is determined by the following function Range= 1 2 𝑣 sin(2 𝜃) 32 0
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Explanation & Answer

Hi! Please see the following solution... If you have a question, please let me know :)

Write a short essay explaining to a classmate how to evaluate the six trigonometric functions of
any angle θ in standard position. Include in your essay an explanation of reference angles and
how to use them, the signs of the functions in each of the four quadrants, and the trigonometric
values of common angles. Include figures or diagrams in your essay.
ANSWER:
The six trigonometric functions are sine
(sin), cosine (cos), tangent (tan), cosecant (csc),
secant (sec), and cotangent (cot). These functions
are ratios based on the lengths of the sides of a
right triangle; and these ratios are constant with the
angles.
Sine of an angle can be expressed as the angle's
opposite side over the hypotenuse, or opp/hyp.
Here are all of the formulas:
Sin = opp/hyp;
Cos = adj/hyp; Tan =
opp/adj;
Csc = hyp/opp; Sec = hyp/adj; Cot =
adj/opp;
As we can see, the cosecant, secant, and
cotangent are just inverses of the three primary
functions of sine, cosine, and tangent.
...


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