IMAGE 1: Find the value of the indicated trigonometric ratio cos α IMAGE 2: Find the value of the indicated trigonometric ratio sin β
IMAGE 3: Find the value of the indicated trigonometric ratio cot γ
IMAGE 4: Find the value of the indicated trigonometric ratio tan α (WORTH 30 POINTS!) Thanks!

28.07° ; 70.53° ; 53.13° ; 36.87°

Step-by-step explanation:

Using PYTHAGORAS RULE :

IMAGE 1:

value of cos α equals :

cos α = Adjacent / Hypotenus

cos α = 15 / 17

cos α = 0.88235

α = cos^-1 (0.88235)

α = 28.07°

IMAGE 2:

sin β = Opposite / Hypotenus

sin β = 14√2 / 21

sin β = 0.9428

β = sin^-1(0.9428)

β = 70.53°

IMAGE 3:

From trigonometry :

cot = 1 / tan

Tan = Opposite / Adjacent

Therefore, Cot = Adjacent / Opposite

cot γ = 3/4

cot γ = 0.75

γ = cot^-1 (0.75)

γ = 53.13°

IMAGE 4:

tan α = Opposite / Adjacent

tan α = 15 / 20

tan α = 0.75

α = tan^-1 (0.75)

α = 36.87°

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

b. 2 and 4

step-by-step explanation: