Mathematical Investigations IV
Name:
Mathematical Investigations IV
Trigonometry - Beyond the Right Triangles
Trigonometry Equations
Solve each equation, finding all solutions exactly in radians, without your calculator.
2sin( x)  1  0
1.
2.
4cos2 ( x)  1  0
3.
tan 2 ( x)  3
5.
2 cos(3x) +
3=0
4.
sin(2 x)  2sin( x)
6.
2sin 2 (3x)  sin(3x)
Trig. 12.1
Rev. S08
Mathematical Investigations IV
Name:
Use identities to help solve the following. Give answers in radians, without your calculator.
7.
sin (2x) = sin (x)
8.
cos  2 x   1  sin( x)
9.
sin(2 x)  tan( x)
10.
2 cos( x)  3  sec( x)  0
Solve each equation using a calculator. Round answers to the nearest hundredth of a radian.
11.
3 sin x = cos x
12.
Trig. 12.2
12sin2 x  cos x  11  0
Rev. S08
Mathematical Investigations IV
Name:
13.
2sec2 x  tan x  5  0
14.
sin (2x) cos x + sin x cos (2x) = 0.2
Beware! Not all equations have "nice" answers.
15.
Consider the equation cos x = x
a.
Graph y = cos x and y = x.
Determine the point of
intersection of these graphs.
b.
Consider the sequence:
k
if n  1

an  
cos(an1 ) if n  1
Use recursion to find the fixed point.
Then compare your answer with the point
of intersection found in part a.
Find all solutions such that 2  x  2 . (Round answers to the nearest hundredth.)
16.
3 cos x = 2 + sin x
17.
sin (3.4x) = sin x (Find some solutions.)
Trig. 12.3
Rev. S08