Question

If sin a = .25 and cos b = .25, which of the following is sin b/2 + cos a/2
A. 1.60
B. 1.32
C. .26
D. 1.06

Answer 1

sin(a) = 0.25

sin^2(a) = (0.25)^2 ... square both sides

sin^2(a) = 0.0625

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sin^2(a) + cos^2(a) = 1

0.0625 + cos^2(a) = 1

cos^2(a) = 1 - 0.0625

cos^2(a) = 0.9375

sqrt( cos^2(a) ) = sqrt(0.9375)

cos(a) = 0.9682458

Answer 2

so if sin(a) = 0.25, then cos(a) = 0.9682458 (approximately)

Answer 3

use this idea to find sin(b)

Answer 4

what would the equation look like? im confused on how to set it up.

Answer 5

@jim_thompson5910

Answer 6

cos(b) = 0.25

cos^2(b) = 0.0625

then you plug it into

sin^2(b) + cos^2(b) = 1

and solve for sin(b)

Answer 7

Im still confused. Sorry i suck at math @jim_thompson5910

Answer 8

basically the same steps will be followed, but instead of 'a' you use 'b'

Answer 9

sin^2(b) + cos^2(b) = 1

sin^2(b) + 0.0625 = 1

sin^2(b) = 1-0.0625

sin^2(b) = 0.9375

sin(b) = sqrt(0.9375)

sin(b) = 0.9682458

Answer 10

so then I take sin b/2 and cos a/2 and add them? @jim_thompson5910

Answer 11

it'd look like this, sin(0.9682458/2) + cos(0.9682458/2) @jim_thompson5910

Answer 12

now you would use the identity

sin(b/2) = sqrt( (1-cos(b))/2 )

so,


sin(b/2) = sqrt( (1-cos(b))/2 )

sin(b/2) = sqrt( (1-0.25)/2 )

sin(b/2) = sqrt( 0.75/2 )

sin(b/2) = sqrt( 0.375 )

sin(b/2) = 0.6123724

Answer 13

okay im catching on @jim_thompson5910

Answer 14

cos(a/2) = sqrt( (1+cos(a))/2 )

cos(a/2) = sqrt( (1+0.9682458)/2 )

cos(a/2) = sqrt( (1.9682458)/2 )

cos(a/2) = sqrt( 0.9841229 )

cos(a/2) = 0.992029687

Answer 15

0.9682458+0.6123724 its gonna be A @jim_thompson5910

Answer 16

correct