Trigonometry

2.61

(Assuming 100 is 100 degrees)

cos 100 degrees is equal to - sin 10 degrees.

In radians, this is - sin (pi/18).

Approximating pi as 22/7, this is - sin (11/63)

Using four terms of a Taylor series, this is approximately:
- (11/63) + (11/63)^3 /6 - (11/63)^5 / 120 + (11/63)^7 / 5040.

- (11/63) + (11^3/63^3) /6 - (11^5/63^5) / 120 + (11^7/63^7) / 5040.

Rewriting the fractions with the common denominator 63^7:
- (11*63^6/63^7) + (11^3*63^4/63^7) /6 - (11^5*63^2/63^7) / 120 + (11^7/63^7) / 5040.

Rewriting again with common denominators of 5040:
- 5040*(11*63^6/63^7)/5040 + 840*(11^3*63^4/63^7)/5040 - 42*(11^5*63^2/63^7) / 5040 + (11^7/63^7) / 5040.

Now add it all up:
[- 5040*11*63^6 + 840*11^3*63^4 - 42*11^5*63^2 + 11^7] / (5040*63^7)

Now, some seriously long multiplication gives:
(- 3466302962466960 + 17612440516440 - 26846879598 + 19487171) / 19852462421401680

Some really easy addition:
-3448717349342947 / 19852462421401680

And finally, do the long division:
-0.17371735939 ... and so on.

The actual value is -0.17364817766693034885171662676931

So, I got 3 decimal places right. Maybe use a better approximation of pi (like 355/113) and more terms of the Taylor series. But you get the picture.

Not certain but calculator says 0.577, may have something to do with circle quadrants ie 210 is 30 degrees into third quadrant of circle (tan 30 = 0.577)

see google - tan in circle, then scroll to sin, cos, tan

If the 49.5 is in radians, then sin 49.5 ≈ −0.693 and so yes.

If the 49.5 is in degrees, then sin 49.5o ≈ 0.760

If the 49.5 is in gradians, then sin 49.5 ≈ 0.702

If the 49.5 is in some other angle measurement, then you'll have to decide as I only know Degrees, Radians and Gradians angle measures.

In Degrees, one full turn is 360o

In Radians, one full turn is 2π radians ≈ 6.283 radians

In Gradians, one full turn is 400 gradians.

Radians are most useful in calculus.

In fact you've used radians without realising it:

The length of an arc of angle θ of a circle of radius r is θr when θ is measured in radians; the length of an arc of a circle round one full turn (ie the circumference of a circle) is θr = 2πr since one full turn is 2π in radians.

You also need an equation for y in order to convert to rectangular form.

Need the fundamental identities here.

tan(X) = sin(X)/cos(X)

sec(X) = 1/cos(X)

so

tan(X)/sec(X)

same as,

sin(X)/cos(X) * cos(X)/1

cancel the cos(X)

= sin(X)

---------------simplest form

Square the two smaller sides and add them together. Take the square root of the answer. If that is the same as the third side then you have a right angled triangle and if not, then you have not.

All you have to do is to select the values you want to have compared with Excel. Then click on Insert on the top, then Scatter, then Scatter with only markers. After this, you can give name to the axises, but then in the Layout section you have to select the regression type of the trendline as well.

sin is short for sine. Sin(x) means the ratio of the side of a right triange opposite the angle 'x' divided by the length of the hypotenuse.

cos is short for cosine. Cos(x) is equal to the similar ratio of the side adjacent to the angle 'x' divided by the length of the hypotenuse.

tan is short for tangent. Tan(x) is equal to the ratio of the opposite side divided by the adjacent side. This is the same as sin(x)/cos(x).

No. An inclinometer only measures vertical angle with respect to gravity. A theodolite adds measurement of horizontal angle to that measurement.

Suppose the sides are a, b and c with c being the hypotenuse.

Then 1/2*a*b is the area which is known. Therefore b = 2*area/a

Also, by Pythagoras, c = sqrt(a2 + b2) so that, using the previous result, c can be expressed in terms of a.

So, you now have a + b + c = perimeter where both b and c can be expressed in terms of a.

This gives a quadratic equation that can be solved for a. The two solutions are a and b, since flipping the triangle will swap the base and height.

sin-1(0.707) = 44.99134834 or about 45 degrees

arctan(0.5)

in degrees = 26.6 degrees

=====================================( you could call it 0.5 radians )

Assuming you know the angle of ascension, and the base, you can calculate the height by recalling that tangent theta is height over base. Simple algebra from there: height is tangent theta times base.

Satellite dishes are paraboloid in shape - that is, a parabola (a quadratic curve) rotated around its axis.

The shape has the property that rays entering it are reflected to its focus of the paraboloid. If the receiver is placed at that point, the signal is picked up from the broadcasting satellite over a wide field of view.

1.570796327

Sin(30) = 1/2

Sin(45) = root(2)/2

Sin(60) = root(3)/2

Cos(30) = root(3)/2

Cos(45) = root(2)/2

Cos(60) = 1/2

Tan(30) = root(3)/3

Tan(45) = 1

Tan(60) = root(3)

Csc(30) = 2

Csc(45) = root(2)

Csc(60) = 2root(3)/3

Sec(30) = 2root(3)/3

Sec(45) = root(2)

Sec(60) = 2

Cot(30) = root(3)

Cot(45) = 1

Cot(60) = root(3)/3

Allied angles are found on the transversal line that cuts through parallel lines and the 2 angles add up to 180 degrees

sin 2θ = 2(sin θ)(cos θ)

cos 2θ = (cos θ)2 - (sin θ)2

cos 2θ = 2(cos θ)2 - 1

cos 2θ = 1 - 2(sin θ)2

tan 2θ = 2(tan θ)/[1 - (tan θ)2]

sin θ/2 = ±√[(1 - (cos θ))/2]

cos θ/2 = ±√[(1 + (cos θ))/2]

tan θ/2 = ±√[(1 - (cos θ))/(1 + (cos θ))] ; cos θ ≠ -1

tan θ/2 = [1 - (cos θ)]/(sin θ)

tan θ/2 = (sin θ)/[1 + (cos θ)]

It is 1.

I'm not sure exactly what this question is asking, but I will attempt to answer.

An angle on the unit circle is created by drawing a straight line from the origin to a point on the circle.

The x-coordinate of a point corresponds to the cosine of the angle.

For example: cos(90o) = 0

The y-coordinate of a point corresponds to the sine of the angle.

For example: sin(270o) = -1

Rewrite it as cosh/sinh

Volume of pyramid = 1/3 Base x Height

100 = 25h/3

25h = 300

height = 12cm

cos(30)cos(55)+sin(30)sin(55)=cos(30-55) = cos(-25)=cos(25)

Note: cos(a)=cos(-a) for any angle 'a'.

cos(a)cos(b)+sin(a)sin(b)=cos(a-b) for any 'a' and 'b'.

The answer is given below: