Trigonometry Answers

4. Use the appropriate compound angle formula to determine the exact value of each expression

a) sin ( pi + Pi over 6 )
b) tan ( Pi over 4 + Pi )
c) cos ( -Pi - pi over 4 )

Determine the exact value of each trigonometric ratio

a) sin 75 degree
b) tan 5pie over 12
c) sin -pie over 12

Express each angle as a compound angle, using a pair of angles from the special triangles

a) 75 degrees
b) pie over 12
c) 5 pie over 6

Rewrite each expression as a single trigonometric ratio, and then evaluate the ratio ( show full work )

1a) tan 170• - tan 110• / 1+ tan 170• tan 110•

b) cos 5pie/12 x cos pie over 12 + sin 5pie over 12 x sin pie over 12

Isosceles triangle is similar to the Isosceles spherical tringale? Justify the answer

From a ship two lighthouses bear N 40o
E. After the ship has sailed 15 miles on a course of 135o
, they bear
10o
and 345o
, respectively. Find the distance between the two lighthouses.

Prove that, If 2 angles of a spherical triangle are equal, then the triangle is an isosceles spherical triangle.

1.) Isosceles triangle is similar to the Isosceles spherical triangle? justify your answer.
2.) An isosceles spherical triangle has an angle A=B= 54° and side b = 82°. Find the measure of the third angle.
3.) Determine the value of angle B of an isosceles spherical triangle ABC whose given parts are b=c= 54°28’ and a = 92°30’
4.) Solve for the side b of a right spherical triangle ABC whose parts of an isosceles spherical triangle are a = 46°, b = 75° and C = 90°.

PROBLEM 1

A navigator sights a lighthouse bearing North-East and distant 10
miles. After sailing eastward 5 miles, he finds that the lighthouse is
8 miles away. Find the new bearing of the lighthouse at the ship.

PROBLEM 2

A ship sails from port “A” due south. After sailing 5 miles it changes
course and sailed straight 8 miles on course 1350 true. How far is the
ship in its present position from port “A”?

PROBLEM 3

Two ships A and B leave port at the same time; Ship A steaming on
course 230
o 35’ at 10 knots and B steaming on course 800 true at 15
knots. Find the distance between them at the end of one hour.

Find the missing parts of an isosceles spherical triangle.
1.) a = b = 78°20’’ C = 118°50’
2.) A = B = 95°5’ C = 100°10’
3.) B = 72°48’ b = 64°52’
4.) A = C = 50°10’ c = 95°
5.) B = C = 78°44’ b = 18°16’