Find cos 2y + Questions on Double & Half Angles.?

1.) If cos y = 1/2, and 3π/2 %26lt; y %26lt; 2π, find cos 2y





2.) If tan B = 4/3, and B lies in Quadrant III, find sin(B/2)





3.) The Expression 2sinx cosx is equivalent to which of the following:


a. 2sinx


b. sin 2x


c. cos 2x


d. tan 2x





4.)The expression 2cos^2(15°)-1 has the same value as:


a. sin 15°


b. cos 15°


c. sin 30°


d. cos 30°





5. If siny = -(7/25), find cos 2y





6. If sin B = 0.6, and B terminates in Quadrant II, find cos (B/2)





7. If cos A = -(5/13) and π %26lt; A %26lt; 3π/2, find cos(1/2)A

Find cos 2y + Questions on Double %26amp; Half Angles.?
1)


cos 2y


= 2 cos^2 y – 1


= 2 (1/2)^2 - 1


= 2 (1/4) - 1


= (1/2) - 1


= -1/2





2)


Tan B = 4/3


then you have a 3-4-5 right triangle.


Sin B = -4/5


Cos B = -3/5





sin (B/2) = +- sqrt [(1 - cos B)/2]


= +- sqrt [(1 - (-3/5)) / 2]


= +- sqrt [(1 + 3/5) / 2]


= +- sqrt [(8/5)/2]


= +- sqrt (4/5)





3)


sin 2x





4)


cos (2*15) = cos 30





5)


cos 2y = 1 - 2sin^2 y


= 1 - 2(-7/25)^2


= 1 - 2(49/625)


= 1 - 98/625


= (625 - 98)/625


= 527/625





6)


if sin B = 0.6 = 6/10


then cos B = -8/10 (use pythagorean theorem to find that.)


cos (b/2) = +- sqrt [(1 + cos b)/2]


= +- sqrt [(1 + -0.8)/2]


= +- sqrt (0.2/2)


= +- sqrt (0.1)





7)


cos (A/2) = +- sqrt [(1 + cos A)/2]


= +- sqrt [(1 + (-5/13)) / 2]


= +- sqrt [(8/13)/2]


= +- sqrt (4/13)