Trigonometry

tan(24 deg) = 0.4452 approx.

sin A = -x/y

Since the sine is the ratio of the opposite leg to the hypotenuse, let's assume the opposite leg's length is -x and the hypotenuse's length is y. Let's call the adjacent leg's length z. So:

(-x)2+z2=y2

z2=y2-(-x)2

z2=y2-x2

z=√(y2-x2)

cos A = z/y = √(y2-x2)/y

cos x - 0.5 = 0

⇒ cos x = 0.5

⇒ x = 2nπ ± π/3

No. But sin2a equals 1 minus cos2a ... and ... cos2a equals 1 minus sin2a

0.999843309

By using The Napier's rule

It is 1.

(2x-5) (x-1)

If a kind of lizards get doubled in its population within 50 months, what will be the duration for them to get tripled.

Usually most of us would give the answer as 75 months ie 6 year 3 months.

But the answer is definitely wrong.

The right answer will be 6 years 7 months and 7 days nearly.

This because of exponential growth.

1 meter is 100 cm

Hence it will take half of 200cm to make 1 meter

An angle is positive when it is measured in a counter-clockwise direction. It is negative when it is measured in a clock-wise direction.

Shack comes from a pro basket ball player named Shackquille O'Neil(Shackquille might not be spelled right).

A full rotation takes 360 degrees. 1309 divided 360 is a little over 3. That mean that it requires 3 full rotations plus change. 1309 - 3(360) = 131. 131 degrees, which is greater than 90 but smaller than 180, is found in the second quadrant.

Yes.

Down

range of y=sin(2x) is [-1;1]

and in generally when is y=sin(k*x) (k=....-1,0,1....) range is always [-1;1] and the period is w=(2pi)/k

a = 0, b = 0.

The expression "cot theta = 1.5 sin theta" can be rewritten using the definitions of trigonometric functions. Since cotangent is the reciprocal of tangent, we have cot(theta) = cos(theta) / sin(theta). Therefore, the equation becomes cos(theta) / sin(theta) = 1.5 sin(theta), leading to cos(theta) = 1.5 sin^2(theta). This relationship can be used to find specific values of theta that satisfy the equation.

6.25

Show that sec'x = d/dx (sec x) = sec x tan x.

First, take note that

sec x = 1/cos x;

d sin x = cos x dx;

d cos x = -sin x dx; and

d log u = du/u.

From the last, we have du = u d log u.

Then, letting u = sec x, we have,

d sec x = sec x d log sec x; and

d log sec x = d log ( 1 / cos x )

= -d log cos x

= d ( -cos x ) / cos x

= sin x dx / cos x

= tan x dx.

Thence, d sec x = sec x tan x dx, and

sec' x = sec x tan x,

which is what we set out to show.

6

No.

tangent tables are used to find values of all angles..precisely..like tan 15 degress and 25 minutes.