Given that \tan\theta =\frac{12}{35}tanθ= 35 12 and that angle \thetaθ terminates in quadrant \text{III}III, then what is the value of \cos\thetacosθ?

Step-by-step explanation:

Given

Quadrant: 3rd

Required

Determine

This question will be solved using the Pythagoras theorem

The tangent of an angle is calculated as thus;

Comparing

to

We can conclude that

Substitute these values in the Pythagoras formula

Square root of both sides

SInce is in the 3rd quadrant, then

Where and

4410

Step-by-step explanation:

To find the area of a square or rectangle, all you need to do is multiply the length times the width:

L × W = A

The lengh is 100, and the width is 50

100 × 50 = 5000

However, in this problem, we also have other shapes in the rectangle. To find the area of JUST the green, we need to subtract the areas of the two circles and small blue rectangle.

First, let's get the two circles over with. To find the area of a circle, use this formula:

A = π      r is the radius, which in this case, is 6

A = π

A = 113       This isn't the exact answer, the exact answer would be 113.0973...

Now let's multiply the area of one of those circles by 2, since we have 2 circles:

113 × 2 = 226

Finally, we have to find the area of the blue rectangle. This is simple, just use the formula from the very beginning:

26 × 14 = 364

The last thing to do is to subtract the areas of the two circles and blue rectangle from the area of the entire thing:

5000 - (226 + 364) = 4410