Find the six trigonometric function values of the angle θ in standard position, if the terminal side of θ is defined by x + 2y = 0, x ≥ 0.

Step-by-step explanation:

First, we need to draw the terminal position of the given angle. To do so, we need to find a point that lies on the straight line

If we choose (we can do so because of the condition , which means that any positive value is suitable for ), then we have

Therefore, the terminal side of the angle  is passing through the origin and the point   and now we can draw it.

The angle    is presented below.

The distance of the point   from the origin equals

Now, we can determine the values of the six trigonometric function, by using their definitions.

if x = 1, then the answer is 3.5

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.