If cos a = 0.465 and sin b = 0.131 (both angles are acute).

Find the values for:
cos (a+b)=
cos(a-b)=

Please show the steps

Correct  cos (a + b) = 0.345  and cos (a - b) = 0.577

Step-by-step explanation:

If both angles are acute, this means that they belong to the first quadrant in which all trigonometric functions are positive.

We first need to know the basic trigonometric equation or identity:

sin²α + cos²α = 1

given: cos a = 0.465 and sin b = 0.131

we must first calculate sin a and cos b

sin²a = 1 - cos²a ⇒ sin a = √ 1 - cos²a = √1- 0.465² 0 √1 - 0.216 = √0.784

sin a = 0.885

cos²b = 1 - sin²b ⇒  cos b = √1 - sin²b = √1 - 0.131² = √1 -  0.017 = √0.983

cos b = 0.991

cos (a + b) = cos a · cos b - sin a · sin b =  0.465 · 0.991 - 0.885 · 0.131

cos (a + b) = 0.461 - 0.116 = 0.345

cos (a + b) = 0.345

cos (a - b) = cos a · cos b + sin a · sin b =  0.465 · 0.991 + 0.885 · 0.131

cos (a - b) = 0.461 + 0.116 = 0.577

cos (a - b) = 0.577

God is with you!!!

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

step-by-step explanation: 4 cause 2+2=4