1. Solve, finding all exact solutions in [0, 2π). a) 3c

1. Solve, finding all exact solutions in [0, 2π).
a) 3cos(2x)-2sinx^(2)xcos(2x)=0
b) tan(2x + π/6) = -1
Solution 1a: Given .
Now,
Sing zero- factor property we get
Either,
Since,
Since,
Since,
Hence from equation (1), the only solution in are
Solution 1b: Given
Now,
Hence, the only solution in are
2. Solve the triangle(s), if possible. Round each final answer to the nearest hundredth
ß = 30°; b = 60; a = 100. (Side a is opposite angle α. Side b is opposite angle β.)
Solution: Given . By sine rule
3. Side a = 40 ft., side b = 30 ft., side c = 12 ft. (Side a is opposite angle α. Side b is
opposite angle β. Side c is opposite side ϒ.
Solve the triangle. Round each final answer to the nearest hundredth.
Find the area of the triangle.
Solution: Given side . The perimeter

By heron’s formula, the area of triangle is
4. Station A is 3.8 miles south of Station B. The bearing from Station A to a ship is
S42°W. The bearing from Station B to the same ship is S26°W. Find the distance
from Station B to the ship, to the nearest tenth of a mile. Show a diagram of any
triangles you use in your solution, with sides and angles labeled.
Solution:
The angle made at ship is
So by sine rule