suppose for an angle theta in a right triangle cos theta = C. Sketch and label this triangle, and then use it to write the other five trig functions of theta in terms of C.

Step-by-step explanation:

Given that:

is an angle in a right angled triangle.

and

To find:

To draw the triangle and write other five trigonometric functions in terms of C.

Solution:

We know that cosine of an angle is given by the formula:

Here, we are given that OR

i.e. Base = C and Hypotenuse of triangle = 1

Please refer to the right angled triangle as per given statements.

, with base PR = C units

and hypotenuse, QP = 1 unit

is the right angle.

Let us use pythagorean theorem to find the value of perpendicular.

According to pythagorean theorem:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.