Trigonometry Answers

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A tower, 28.4ft high must be secured with a guy wire anchored 5ft. from the base of the

tower. What angle will the guy wire make with the ground?


Use the diagram to find the angle measures of the triangle. Recall that the sum of the angle measures of a triangle is 180°

x=

(x+4)=

9x=



if P (2π/3) = ( -1/2 , /3/2) then cos Ø =?



Prove the following identities



(a)(cos t)(tan t)(csc t) =1


Explain the Pythagorean Theorem, its proofs and applications.


APPLICATIONS OF TRIGONOMETRY

  1. An astronomer finds that the distance from planet A to galaxy B is 30 light years and the distance from A to galaxy C is 80 light years. the angle between distance AB and distance AC is measured to be 60 degree.

A. how far apart are the galaxies? (distance of galaxy B to galaxy C); and

B. Find the angle between distance AB to distance BC.

*show complete solution.


If cos(A-B) = cos 15° and cos(A+B)= cos 75° , the values of A and B. Hence without using a calculator and by using the sum and difference formula, show that cos 15° - cos 75° = 2 sin 45° sin 30°


P(3,-3) lies on the terminal arm of an angle in standard position.

a. Draw a sketch of the principal angle (θ) in standard position. Label θ AND the related acute

angle, RA. [2 marks]

b. Determine the exact primary trig ratios for θ. Show ALL your work. You do not need to

rationalize the denominator, but you must simplify your radical and your ratios. [5 marks]

c. Determine the values of the principal angle and related acute angle to the nearest degree.


1. A commercial ship is heading due North


at 12.0 km/hr but drifts westward at 5.0


km/hr. determine the magnitude and


direction of the resultant velocity of the


ship.




2. Find the resultant of the following


vectors.


A = 30 m at 30° with the x-axis


B = 20 m at 120° with the x-axis


C = 10 m at 225° with the x-axis.


Show that d= 2v² costheta sintheta(0_x)/gcos²thetax


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