Download Double Angles

Mathematical Investigations IV
Name:
Mathematical Investigations IV
Trigonometry - Beyond the Right Triangles
Double Trouble
** Optional problems for extra practice.
Double Angle Formulas:
I.
sin (2)
Write the sum formula for sin    


Replace  by . Simplify.
sin (2) =
II.
cos (2)
Write the sum formula for cos    


Replace  by . Simplify.
cos (2) =
To find an alternate form, replace sin2 by 1 – cos2 and simplify.
cos (2) =
To find a second alternate form, in the original expression two lines above, replace
cos2 by 1 – sin2 and simplify.
cos (2) =
III.
tan (2)
Write the sum formula for tan    


Replace  with . Simplify.
tan (2) =
Trig. 10.1
Rev. S06
Mathematical Investigations IV
Name:
1.
2.
Use the double-angle formulas to find exact values for each of the following.
a.
sin 120°
**b.
c.
tan 120°
**d.
tan 300°
e.
cos 300°
**f.
sin 300°
Use the Angle Sum Formulas (from worksheet 8.2) to find the exact values for each of the
following:
a.
3.
4.
cos 120°
cos 75°
Let sin  =

b.
sin 75°
1

where 0 <  < . Find the value of sin (2
3
2

Let tan     3 and tan  =
1
. Find the value of tan.
2
Trig. 10.2
Rev. S06