Mathematical Investigations IV
Name:
Mathematical Investigations IV
Trigonometry - Beyond the Right Triangles
Double Angle Formulae
1. Use the fact that  +  = 2 to find a general formula for sin  2  .
2. Use the fact that  +  = 2 to find a general formula for cos  2  .
3. Rewrite your answer to 2. in terms of only sin   , then again in terms of only cos   .
Double Angle Formulas for Sine and Cosine
sin  2   2sin   cos  
cos  2   cos 2    sin 2  
 2 cos 2    1
 1  2sin 2  
Trig. 10.1
Rev. F09
Mathematical Investigations IV
Name:
4. 4.
a.


Find:
sin =
cos =
sin =
cos =
(8,15)
(-5,-12)
b.
Write out each formula. Then substitute in the values:


sin    
sin  2  
cos     
cos  2  
5.
Simplify and evaluate ( Remember: No calculators. Check your answers with another
student at your table. )
a.
b.
c.
sin40° cos20° + sin20°cos40°
2
2
cos15° +
sin15°
2
2
cos140° cos5° + sin140° sin5°
Trig. 10.2
Rev. F09
Mathematical Investigations IV
Name:
6.
Find the period of each of the following trig functions.
a.
y = sin(2x) cos(3x) + sin(3x) cos(2x)
b.
y = cos(3x) cos(–2x) – sin(3x) sin(2x)
7.
8.
Simplify:
a.
sin(x) cos(2x) cos(4x) + sin(2x) cos(x) cos(4x) + sin(4x) cos(3x)
b.
sin(x)
cos(x)

sec(2x) csc(2x)
Find an expression for tan  2  in terms of using tan   .
Trig. 10.3
Rev. F09