Trigonometry
Trigonometric Functions
Given: Cos θ = (3/5), Find: Csc θ

csc theta =   5/4

Step-by-step explanation:

cos theta = 3/5

cos theta = adjacent side/ hypotenuse

Let adjacent side = 3 and the hypotenuse = 5

csc theta =  hypotenuse/ opposite side

We need to find the opposite side

We know that this is a right triangle, so we can use the Pythagorean theorem

(adj)^2 + (opp)^2 = (hyp)^2

3^2 + (opp)^2 = 5^2

9+ (opp)^2 = 25

Subtract 9 from each side

9-9+ (opp)^2 = 25-9

(opp)^2 = 16

Take the square root of each side

sqrt( (opp)^2) = sqrt(16)

opp = 4

csc theta =  hypotenuse/ opposite side = 5/4

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

51

step-by-step explanation:

73-22=51 the   mass number minus the amount of protons gives you the amount of neutrons