Directions: Complete each ratio table.

Please explain as well, solve the trigonometric equation

aliina [53]

Given:

The trigonometric equation is:

$\tan x\sin x=\tan x\cos x$

To find:

The solutions for the given equation over $0^\circ$ .

Solution:

We have,

$\tan x\sin x=\tan x\cos x$

It can be written as

$\tan x\sin x-\tan x\cos x=0$

$\tan x(\sin x-\cos x)=0$

$\tan x=0$ and $(\sin x-\cos x)=0$

The solutions over $0^\circ$ are:

$x=90^\circ,180^\circ$ and $\sin x=\cos x$

$x=90^\circ,180^\circ$ and $x=45^\circ, 225^\circ$

Therefore, the correct option is D.

3 0

3 years ago

Which ratio is equivalent to 2:8

Serhud [2]

1:4 is equal to 2:8, it's a simplified version.

6 0

3 years ago

Read 2 more answers

Help with this please

Paha777 [63]

I think it is B
hope this helps

6 0

3 years ago

In a certain town there were 403 robberies last year. This year the number of robberies has gone down 35%. How many robberies we

Maurinko [17]

Answer:

262

Step-by-step explanation:

From the Question, we know that:

In a certain town there were 403 robberies last year. This year the number of robberies has gone down 35%.

Step 1

Find the amount decreased

35% × 403

= 35/100 × 403

= 141.05

Step 2

The amount of robberies this year is:

= 403 - 141.05

= 261.95

Approximately to the nearest whole number = 262

3 0

3 years ago

Find the value of angle x , angle y, and angle z in figure.

Lynna [10]

$\bf \underline{★ Solution-} \\$

In the given figure, we are given with two lines which are parallel to each other. We are also given with two lines which forms a triangle and also forms as a transversal lines to the parallel lines. We are also given that the given triangle is an isosceles triangle. So, we can say that the other angle in the triangle also measures 75°.

Now, let's find the value of the ∠x.

We know that the alternate angles in the parallel line always measures the same as the one which is in it's alternate side. So,

$\sf \leadsto \angle{x} = {75}^{\circ}$

Now, let's find the value of the ∠z.

We know that, all the angles in a triangle always adds up to 180°. In the given triangle, we are given with two angles, so we can easily find the third angle.

$\sf \leadsto {75}^{\circ} + {75}^{\circ} + \angle{z} = {180}^{\circ}$

$\sf \leadsto {150}^{\circ} + \angle{z} = {180}^{\circ}$

$\sf \leadsto \angle{z} = 180 - 150$

$\sf \leadsto \angle{z} = {30}^{\circ}$

Now, let's find the value of the ∠y.

We know that all the angles that forms a straight line always equals up to 180° (or) the the straight line angle always measures 180°. So, we can find the value of the ∠y by this concept.

$\sf \leadsto {75}^{\circ} + {30}^{\circ} + \angle{y} = {180}^{\circ}$