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Trigonometry

Trigonometry is a field of mathematics. It is the study of triangles. Trigonometry includes planar trigonometry, spherical trigonometry, finding unknown values in triangles, trigonometric functions, and trigonometric function graphs.

3,810 Questions

How would you show all work for 1 minus 2cos squared theta?

You could not.

1 - 2cos2theta is an expression which cannot be solved nor evaluated without information about theta. If you need to show its equivalence to another expression then it is necessary to know what the other expression is.

How do you change cos theta to sin theta?

One relationship is:

cos(x) = sin(90° - x)

if you use degrees. Or in radians:

cos(x) = sin(pi/2 - x)

Another relationship is the pythagorean identity.

What is the sin cos tan formula if i don't have an ti 84 calc?

The answer depends on what the triangle is and what information you have. The formulae which are available for right angled triangles are not applicable for triangles which do not have a right angle. Trigonometric ratios are defined for angles, whether or not the shape is a triangle.

In general, there is no simple method for working out these ratios without a calculator (or reference tables).

If x is the angle, measured in radians, then

sin(x) = x - x^3/3! + x^5/5! - x^7/7! ...

cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! ...

and

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

But these are hardly calculable without a calculator!

Note that n! = 1*2*3* ... *n for positive integer n.

How do you find the Volume of a triangular block?

You have to find out the area of the base which you find out with perpendicular height times base then time that by the perpendicular height of the pyramid and divide it by 3

What is the derivative of cos pi x plus sin pi y all to the 8th power equals 44?

(cos(pi x) + sin(pi y) )^8 = 44

differentiate both sides with respect to x

8 ( cos(pi x) + sin (pi y ) )^7 d/dx ( cos(pi x) + sin (pi y) = 0

8 ( cos(pi x) + sin (pi y ) )^7 (-sin (pi x) pi + cos (pi y) pi dy/dx ) = 0

8 ( cos(pi x) + sin (pi y ) )^7 (pi cos(pi y) dy/dx - pi sin (pi x) ) = 0

cos(pi y) dy/dx - pi sin(pi x) = 0

cos(pi y) dy/dx = sin(pi x)

dy/dx = sin (pi x) / cos(pi y)

Where does the word eclectic come from?

The word eclectic comes from the Greek words 'ek' meaning 'out' and 'legein' meaning 'choose.' Those words were combined to create 'eklegein' that means 'pick out' and then the word changed to eklektikos and then the 17th century brought about the word eclectic.

How do you solve 2cosx plus 2sinx equals sqrt2 for solutions between 0 and 2pi?

Not easily and, given the limitations of the pathetic browser that we have at our disposal, even less easy. But here goes:You are given that 2cosx + 2sinx = sqrt(2)

Consider "collapsing" the left hand side into a single trig function:

r*sin(x+a) = sqrt(2) ............................................. (A)

that is r*cosxsina + r*sinxcosa = sqrt(2)

comparing coefficients,

rsina = 2 and rcosa = 2

then

sina = 2/r = cosa

and since sin^2 + cos^2 = 1, you have r = 2*sqrt(2)

also, rsina/rcosa = 2/2 = 1 = tana which implies that a = pi/4.


Therefore, equation (A) is 2*sqrt(2)*sin(x+pi/4) = sqrt(2)

so that sin(x+pi/4) = 1/2.......................................(B)

Since 0<= x <= 2*pi

pi/4 < x+pi/4 < 2*pi+pi/4


So the solutions to (B) in the relevant domain are x+pi/4 = 5*pi/6 or 13*pi/6

therefore x = 5*pi/6-pi/4 or 13*pi/6-pi/4

that is x = 7pi/12 and 23pi/12.

Why is 1 hour equals 60 minutes?

One hour is 60 minutes because that is the way it is defined.

When did Sine Totoo end?

Sine Totoo ended on 2009-02-28.

Why does quadrant 2 come before quadrant 1?

It doesn't. Its a matter of interpretation.

When drawing the unit circle, we start at x=1, y=0. As we draw, maintaining a radius of 1 from the origin at x=0, y=0, we proceed counter-clockwise. Initially, both x and y are positive. That is quadrant 1. When x becomes negative at x=0, y=1, that is quadrant 2. When y becomes negative at x=-1, y=0, that is quadrant 3. And when x becomes positive again at x=0, y=-1, that is quadrant 4.

So you see, its all in the perspective of which comes first, and in trigonometry, the vector where theta = 0 comes first, not where your eye just happens to scan from left to right.

A 15 sided shape?

Yes, it can exist - assuming that was your question.

How long must a ladder be to reach the top of a 20 foot wall if the ladder and the wall form a 32 degree angle at the top?

23.58 feet

A+

no its not i just tryed it so yea get your facts right before putting them on here

but i dont even know this so srry for the ppl look for it

What does the word trigonometry identity mean?

An identity is like an equation which is true for all values of the variable.

What is the perimeter of a triangle if its smallest side is 13.62 mm when two of its angles are 71 degrees and 57 degrees?

Its 3rd angle is 52 degrees which is its smallest angle and opposite to its smallest side and by using the sine rule the perimeter of the triangle works out as 44.45 mm to two decimal places