The point (-2,3) is on the terminal side of angel theta, in standard position. what are the values of sine, cosine, and tangent of theta? show all work

Draw a right triangle with horizontal base length 2, vertical length 3.

Use pythagorean thm to find length of hypotenuse:

Now use SOH CAH TOA to find correct trig ratios:

The opposite side is always the vertical side > 3

The adjacent side is always the horizontal side ---> 2

SOH ---> sin = opp/hyp

CAH  > cos = adj/hyp

TOA > tan = opp/adj

the solution is h=10 because you add 9 to each side of the equation.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is