Question

a physicist needs to calculate the exact value of a force(measured in newtons) in the horizontal direction with the expression 25cos75. Simplify the expression to find the exact value

Answer 1

Answer:

25*√((2-√3)/2)

Step-by-step explanation:

Use the identity: cos(x)=sin(90°-x)

cos(75°)=sin(90°-75°)=25sin(90°-75°)

Simplify

25sin(15°)

then write sin(15°) as sin(30°/2)

Use the half-angle identity: sin(x/2)= ((1-cos(x))/2)^(1/2)

((1-cos(30°))/2)^(1/2)     cos(30°)=((3)^(1/2))/2

then plug that in for the cos(30°) and solve

√((2-√3)/2)    multiply by 25

25*√((2-√3)/2)