Use a formula to find the exact values sin(75)+sin(15)?

Answer 1

sin s + sin t = 2sin((s + t)/2)cos((s – t)/2)
sin75 + sin15 = 2sin((75 + 15)/2)cos((75 - 15)/2)
sin75 + sin15 = 2sin(90/2)cos(60/2)
sin75 + sin15 = 2sin45cos30
sin75 + sin15 = 2(1/2)√2(1/2)√3
sin75 + sin15 = (1/2)√6

Answer 2

Sin 75 Sin 15

Answer 3

ASSUMING THE VALUES ARE IN DEGREES:

SIN(75°) + SIN(15°)

CAN BE SIMPLIFIED TO:

(√6/4 + √2/4) + (√6/4 - √2/4)

THEREFORE, THE ANSWER IS:

√6/2

OR

1.224744871

Answer 4

you employ the a million/2-perspective formula: sin(theta/2) = +/- sqrt((a million-cos(theta))/2). 30 stages is between the ordinary angles that maximum trig instructors anticipate you to memorize; its cosine is sqrt(3)/2. So sin(15) = sin(30/2) = +/- sqrt(a million-sqrt(3)/2)/2) = +/- sqrt(a million/2 - sqrt(3)/4). To get the sign, you basically ought to apply some easy experience. 15 stages is interior the 1st quadrant of the unit circle, so its sine and cosine ought to the two be useful. provided that a sq. root is often useful, all of us understand that sin(15) = sqrt(a million/2 - sqrt(3)/4). i'm going to wager there is a few thank you to simplify that, yet i won't be in a position to think of what it must be.

Answer 5

sqrt=square root

sin(75)+sin(15)
=sin(45+30)+sin(60-45)
=sin(45)cos(30)+cos(45)sin(30)+
sin60cos45-cos60sin45
=(1/sqrt 2)(sqrt 3/2)+(1/sqrt 2)(1/2)+
(sqrt 3/2)(1/sqrt 2)-(1/2)(1/sqrt 2)
=(1/sqrt 2)[sqrt 3/2 +1/2 +sqrt 3/2 -1/2]
=(1/sqrt 2)[2sqrt 3/2]
=sqrt 3 /sqrt 2
=sqrt (3/2) #

Answer 6

use the formula sinC+sinD=2sin{(C+D)/2}*cos{(C+D)/2},simplify and then look into the sine values chart to get exact decimal values.

Answer 7

sinA+sinB=2sin(A+B)/2 cos(C-D)/2
=2sin45*cos30

now look fr these values...