Use double angle formulas to evaluate exact measures of
a) sin(π/12)
b) cos(3π/8)
well sin (π/6)= 1/2 , cos (π/6) = (sqrt 3 )/ 2
so sin( π/6 /2) = sqrt [ (1-cos π/6)/2 ]
=sqrt [ (1 - (sqrt 3 )/ 2 ) /2
=sqrt [ (2 - sqrt 3 ) /4 ]
= (1/2) sqrt (2 -sqrt 3) =.259
yes, sin 15 degrees = .259
You do the next one.
why would i ask if i cant do it
thanks though !!
can**
To evaluate the exact measures of sine and cosine using the double angle formulas, we need to express the given angles in terms of double angles. Let's start with sine.
a) sin(π/12):
The double angle formula for sine is:
sin(2θ) = 2sin(θ)cos(θ)
We can rewrite π/12 as a double angle by dividing it by 2:
π/12 = (π/6)/2
Now, we can substitute π/6 into the double angle formula:
sin(π/12) = 2sin(π/6/2)cos(π/6/2)
Since sin(π/6) = 1/2 and cos(π/6) = √3/2, substituting these values:
sin(π/12) = 2sin(π/6/2)cos(π/6/2)
= 2(1/2)(√3/2)
= √3/2
Therefore, the exact measure of sin(π/12) is √3/2.
b) cos(3π/8):
The double angle formula for cosine is:
cos(2θ) = cos^2(θ) - sin^2(θ)
We need to express 3π/8 as a double angle. Dividing it by 2, we get:
3π/8 = (3π/4)/2
Now, we substitute 3π/4 into the double angle formula:
cos(3π/8) = cos^2(3π/4/2) - sin^2(3π/4/2)
Since cos(3π/4) = -1/√2 and sin(3π/4) = 1/√2, we can substitute these values:
cos(3π/8) = cos^2(3π/4/2) - sin^2(3π/4/2)
= (-1/√2)^2 - (1/√2)^2
= 1/2 - 1/2
= 0
Therefore, the exact measure of cos(3π/8) is 0.