use the half angle formula to determine the exact values of sin, cos, and tan of the angle.
pie/8
and
pie/12
3 answers
I will be happy to check your thinking on this.
i honestly don't know what to do or how to start anyways
the half-angle formulas let you split an angle in half
there is sin 2A = 2sinAcosA and
cos 2A = cos^2 A - sin^2 A or
cos 2A = 2cos^2 A - 1 or
cos 2A = 1 - 2sin^2 A
I will do the pi/12 angle for you.
pi/6 rads = 30 degrees, and pi/12 = 15 degrees
From the 30-60-90 triangle you should know
sin30 = 1/2 and cos30 = ?3/2
cos 30 = 1 - 2sin^2 15
2sin^2 15 = 1-?3/2
sin ^2 15 = 1/2 - ?3/4
= (2-?3)4
so sin 15 = ?(2-?3)/2
or sin pi/12 = ?(2-?3)/2
now ;use the other version of cos 2A to get cos pi/12
and since tanx = sinx/cosx, divide the two results to get the tangent.
verify your answer with your calculator
for the first pi/8 is half of pi/4 which is 45 degrees
you should know the trig rations for 45 degrees.
there is sin 2A = 2sinAcosA and
cos 2A = cos^2 A - sin^2 A or
cos 2A = 2cos^2 A - 1 or
cos 2A = 1 - 2sin^2 A
I will do the pi/12 angle for you.
pi/6 rads = 30 degrees, and pi/12 = 15 degrees
From the 30-60-90 triangle you should know
sin30 = 1/2 and cos30 = ?3/2
cos 30 = 1 - 2sin^2 15
2sin^2 15 = 1-?3/2
sin ^2 15 = 1/2 - ?3/4
= (2-?3)4
so sin 15 = ?(2-?3)/2
or sin pi/12 = ?(2-?3)/2
now ;use the other version of cos 2A to get cos pi/12
and since tanx = sinx/cosx, divide the two results to get the tangent.
verify your answer with your calculator
for the first pi/8 is half of pi/4 which is 45 degrees
you should know the trig rations for 45 degrees.
1 answer