What is the value of secant theta given the diagram below? a unit circle is shown. a ray intersects point (negative 3, 6) in quadrant 2. theta is the angle formed by the ray and the x-axis in quadrant 1. negative startroot 5 endroot negative startfraction startroot 5 endroot over 2 endfraction startfraction startroot 5 endroot over 2 endfraction startroot 5 endroot

- √5

Step-by-step explanation:

Given that, a ray intersects point (negative 3, 6) in quadrant 2 and we are told to find the value of secant theta.

To get the answer to the question,  

The first step is to find the hypotenuse, we have to use the Pythagoras theorem  where, Hypotenuse = opposite raise to power two + adjacent raise to power.  

(I.e. h= O² + A²)

H = 6² + (-3)2

H = 36 + 9

H = 45

We then convert the answer to surds form.  

H = 3√5

The next step is to find the value of secant theta.  

To get the value of secant theta we will have to divide the hypotenuse by adjacent with a negative sign because of the negative sign in the second quadrant  

We have  

Sec ø = - (hypotenuse/adjacent)  

Sec ø = - (3√5/ 3)

Sec ø = - √5

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option