Trigonometry

cot(15)=1/tan(15)

Let us find tan(15)

tan(15)=tan(45-30)

tan(a-b) = (tan(a)-tan(b))/(1+tan(a)tan(b))

tan(45-30)= (tan(45)-tan(30))/(1+tan(45)tan(30))

substitute tan(45)=1 and tan(30)=1/√3 into the equation.

tan(45-30) = (1- 1/√3) / (1+1/√3)

=(√3-1)/(√3+1)

The exact value of cot(15) is the reciprocal of the above which is:

(√3+1) /(√3-1)

Cotangent is 1 / tangent.

Since tangent is sine / cosine, cotangent is cosine / sine.

Inverse sine is defined for the domain [-1, 1]. Since 833 is way outside this domain, the value is not defined.

-1273 degrees lies in quadrant two. Simply add 360 degrees repeatedly until it becomes positive, giving 167 degrees. Note that is greater than 90 and less than 180, making it quadrant two.

A useful property in Trigonometry is:

tan(x) = sin(x) / cos(x)

So, cos(x) tan(x) = cos(x) [ sin(x) / cos (x)]

= sin(x)

It is approx 0.9725

This may not be the most efficient method but ...

Let the three angle be A, B and C.

Then note that A + B + C = 20+32+38 = 90

so that C = 90-A+B.

Therefore,

sin(C) = sin[(90-(A+B) = cos(A+B)

and cos(C) = cos[(90-(A+B) = sin(A+B).

So that tan(C) = sin(C)/cos(C) = cos(A+B) / sin(A+B) = cot(A+B)

Now, tan(A+B) = [tan(A)+tan(B)] / [1- tan(A)*tan(B)]

so cot(A+B) = [1- tan(A)*tan(B)] / [tan(A)+tan(B)]

The given expressin is

tan(A)*tan(B) + tan(B)*tan(C) + tan(C)*tan(A)

= tan(A)*tan(B) + [tan(B) + tan(A)]*cot(A+B)

substituting for cot(A+B) gives

= tan(A)*tan(B) + [tan(B) + tan(A)]*[1- tan(A)*tan(B)]/[tan(A)+tan(B)]

cancelling [tan(B) + tan(A)] and [tan(A) + tan(B)], which are equal, in the second expression.

= tan(A)*tan(B) + [1- tan(A)*tan(B)]

= 1

It is 1.04

tan(9) + tan(81) = sin(9)/cos(9) + sin(81)/cos(81)= {sin(9)*cos(81) + sin(81)*cos(9)} / {cos(9)*cos(81)} = 1/2*{sin(-72) + sin(90)} + 1/2*{sin(72) + sin(90)} / 1/2*{cos(-72) + cos(90)} = 1/2*{sin(-72) + 1 + sin(72) + 1} / 1/2*{cos(-72) + 0} = 2/cos(72) since sin(-72) = -sin(72), and cos(-72) = cos(72) . . . . . (A) Also tan(27) + tan(63) = sin(27)/cos(27) + sin(63)/cos(63) = {sin(27)*cos(63) + sin(63)*cos(27)} / {cos(27)*cos(63)} = 1/2*{sin(-36) + sin(90)} + 1/2*{sin(72) + sin(36)} / 1/2*{cos(-36) + cos(90)} = 1/2*{sin(-36) + 1 + sin(36) + 1} / 1/2*{cos(-36) + 0} = 2/cos(36) since sin(-36) = -sin(36), and cos(-36) = cos(36) . . . . . (B) Therefore, by (A) and (B), tan(9) - tan(27) - tan(63) + tan(81) = tan(9) + tan(81) - tan(27) - tan(63) = 2/cos(72) – 2/cos(36) = 2*{cos(36) – cos(72)} / {cos(72)*cos(36)} = 2*2*sin(54)*sin(18)/{cos(72)*cos(36)} . . . . . . . (C) But cos(72) = sin(90-72) = sin(18) so that sin(18)/cos(72) = 1 and cos(36) = sin(90-36) = sin(54) so that sin(54)/cos(36) = 1 and therefore from C, tan(9) – tan(27) – tan(63) + tan(81) = 2*2*1*1 = 4

They are such that their squares sum to 6.72 = 44.89

ie if one side is of length x with 0 < x < 6.7

the other side is of length √(44.89 - x2)

This isn't hard to figure out if you know how far you want the base of the ladder from the wall. All you have to do is use the Pythagorean Theorem. The theorem is A2 + B2 = C2. A and B are the short sides and C is the hypotenuse (the side opposite the right angle). When dealing with a ladder, the ladder is the hypotenuse, or the C in the equation. Another way to put the formula is to multiply A by itself and B by itself, add them together, then take the square root of the result.

Decide how far you want the base of the ladder from the building. Multiply that by itself then add that to 169 (that is the square of 13). Then take the square root of that and you get the ideal ladder height. Lets assume 5 feet from the wall. The square of that is 25. 169 plus 25 gives 194. The square root of 194 is 13.928, and we would round up to 14 feet.

If you mean a step ladder, and you are trying to reach a ceiling, then you would need roughly the height of the room minus your own height. You might want to add a tad more. You could make it shorter, but that would not be wise, since you should always avoid the top two steps if possible.

cos20 x cos40 x cos80 = 0.0300 radians

= 0.125 degrees

(the value for radians is given to four decimal places, the value in degrees is exact)

sine 40° = 0.642788

Note: When doing trigonometry, it is highly recommeded that you have a scientific calculator at hand. Also, make sure your calculator is in Degree (D or Deg) mode and not Radian (R or Rad).

To find the cosine of 70o, press 'cos', then type in 70, then press equals. You should get 0.342 (to the nearest 3 decimal places).

If tan(theta) = x

then sin(theta) = x/(sqrt(x2 + 1) so that csc(theta) = [(sqrt(x2 + 1)]/x

= sqrt(1 + 1/x2)

60

You cannot.

A right angled isosceles triangle will always be 90-45-45 so knowing the angles does not add any information. Without knowledge of any one side, you cannot distinguish between the infinitely many similar 90-45-45 triangles.

First, find the ratio of fencepost-height : shadow which is 1.6 : 2.6 . This can also be written as a fraction, 1.6/2.6 . Then, multiply the flagpole's shadow by this ratio:

31.2 x 1.6/2.6 = 19.2

The flagpole is 19.2m high.

The trigonometry way:

On the imaginary right angled triangle formed by the fencepost and its shadow, let the angle at which the hypotenuse meets the ground = θ

sinθ = 1.6/2.6

sinθ = /31.2

x/31.2 = 1.6/2.6

2.6x = 31.2 * 1.6 = 49.92

x = 19.2

The flagpole is 19.2m high.

It is 0.2048*PI radians, approx.

If, at any time, a vertical line intersects the graph of a relationship (or mapping) more than once, the relationship is not a function. (It is a one-to-many mapping and so cannot be a function.)

Theta is just a Greek letter used to denote measurement of angle. Sine is a trigonometric function, i.e., the ratio of the side opposite to the angle theta to the hypotenuse of the triangle. So Sine theta means the value of sine function for angle theta, where theta is any angle.

Sine Pari is Latin for "without equal".

to find the measure of an angle.

EX: if sin A = 0.1234, then inv sin (0.1234) will give you the measure of angle A

My calculator tells me that sin 58 degrees = 0.84805