If sin theta = 2/3 and tan theta < 0, what is the value of cos theta? a) sqrt 5/2 b) -sqrt 5 c) sqrt 5/3 d) -sqrt 5/3

It is given tan theta <0

we know that tan theta is negative ( OR <0 ) in second ( pi/2 to pi )and fourth quadrant ( from 3pi/2 to 2 pi ) only .

Given sin theta = 2/3 which is positive ( first and second quadrant ) value so we can consider second quadrant only

Second quadrant tan( theta ) is <0 and sin( theta ) >0

We know sin ^2 ( theta) + cos^2( theta) = 1

( 2/3) ^2 + cos^2( theta ) = 1

Cos^2 (theta ) = 1- ( 2/3)^2

Cos^2 ( theta ) = 1- (4/9)

Cos^2 (theta ) = ( 9-4) / 9

Cos^2 theta = 5 /9

Cos theta = sqrt 5/3 OR - sqrt 5 /3

BUT Cos is negative in second quadrant

So answer is - sqrt 5/ 3

step-by-step explanation:

from the graph attached below:

domain of graph is the value of x for which the given function profit function p(x) is defined.

(a) the domain represents the number of years for which the outlet will earn a profit.

range of profit function defines the lowest to highest value of profit earned.

(b) the range of this function is (0 , 160 ). for this function, the range represents the outlet's profit earned.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional