Find the exact values of the six trigonometric functions of 0 given the point (5,4) on the terminal side of 0 in standard position.

choice d.  with  sin(theta) =  4 root(41)/41   tan(theta) = 4/5

Step-by-step explanation:

given theta with the terminal point at (5, 4)

It makes sense that  tan (theta) = 4/5   because height : 4 and base is 5.

The hypotenuse length should be:  root( 5^2 + 4^2) = root(25 + 16) = root(41)

so  sin (theta) =   4 /  root(41)   where opposite side over hypotenuse

simplify:   sin (theta) = 4* root(41)/ 41

cos (theta) = 5 /root(41)  =   5*root(41) / 41

cosecant :  csc (theta) = 1/sin(theta) =   root(41)/4

secant:    sec (theta) = 1/cos(theta) =  root(41)/5

cot (theta) = 1/tan(theta) = 5/4

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

circumference divided by 3.141592654 then timesthe radius twice

step-by-step explanation:

circumference divided by 3.141592654 then timesthe radius twice