The coordinates of a point P, located on the terminal side of a trigonometric angle , are given, where . Determine the exact value of sin , cos et tan

Mathematics by Geoffrey

Unit circle and trigonometric identities.

Law of sines and cosines.

Question 1: The coordinates of a point P, located on the terminal side of a trigonometric angle , are given, where . Determine the exact value of sin , cos et tan .

 

  1. a)

 

 

 

 

 

 

b)

 

 

 

 

 

 

  1. c)

 

 

 

 

Question 2: The coordinates of a point P, located on the terminal side of a trigonometric angle , are given, where . Determine the exact value of sin , cos et tan .

 

  1. a) P(6,5) b) P(-2,-5)

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. c) P(2,-4) d) P(3,3)

 

 

 

 

 

 

 

 

 

 

Question 3:Give an equivalent expression for each of the expressions below.

 

  1. a)

 

 

 

 

  1. b)

 

 

 

 

  1. c)

 

 

 

 

 

Question 4: Prove each of the following identities.

 

  1. a)

 

 

 

 

 

 

 

 

 

 

  1. b)

 

 

 

 

 

 

 

 

 

 

 

  1. c)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 5: Determine the measure of the angle shown, to the nearest tenth of a degree.

 

a)

 

 

 

 

 

 

 

 

 

b)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 6: Airport X is located 150 km east of Airport Y. An airplane is approaching from the west 240 km from Airport Y. The line joining airport Y to the plane forms an angle of 23 degrees with the ground. How far is the plane from airport X, to the nearest kilometer?