Trigonometry

It's possible that either the angles or sides are labeled according to length or size.

Assume the angle u takes place in Quadrant IV.

Let u = arctan(-12). Then, tan(u) = -12.

By the Pythagorean identity, we obtain:

sec(u) = √(1 + tan²(u))

= √(1 + (-12)²)

= √145

Since secant is the inverse of cosine, we have:

cos(u) = 1/√145

Therefore:

sin(u) = -√(1 - cos²(u))

= -√(1 - 1/145)

= -12/√145

Otherwise, if the angle takes place in Quadrant II, then sin(u) = 12/√145

That depends on your profession. If you are a math teacher, then you might use a lot of Trig. If you are an engineer, working with forces on any object from different directions, then you would use trig. Electrical engineers use trig. Surveyors use trig.

Surveying the land. Laying out the position of the foundation of the building.

The double angle formula states that sin(2x) = 2sin(x)cos(x), and because sin2(x) + cos2(x) = 1, sin(2x) = 2sin(x)*SQRT(1-sin2(x)). However, that will only give you the correct result when cos(x) is positive. (because SQRT only returns the positive square root)

If, by trigonometry theorem you mean the "fundamental theorem of trigonometry," sin2(x) + cos2(x) = 1, it is actually the Pythagorean Theorem. if you have a right triangle with a hypotenuse of one, sin(x) is one leg, and cos(x) is the other. The Pythagorean Theorem states that a2 + b2 = c2 and therefore sin2(x) + cos2(x) = 1.

There is a trigonometric identity that states that sec2(x) - tan2(x) = 1, for every x. By rearranging this formula we can find that sec2(x) - 1 = tan2(x).

Since there are 2 Pi radians in one complete turn, then the minute hand turns 1.75 * 2 Pi radians in 1.75 hours.

If x2 + y2 = 1, then the point (x,y) is a point on the unit circle.

A Quadrantal angle is an angle that is not in Quadrant I. Consider angle 120. You want to find cos(120) . 120 lies in quadrant II. Also, 120=180-60. So, it is enough to find cos(60) and put the proper sign. cos(60)=1/2. Cosine is negative in quadrant II, Therefore, cos(120) = -1/2.

It is 3 minus 2i

Cosine squared theta = 1 + Sine squared theta

If sin θ = tan θ, that means cos θ is 1 (since tan θ = (sin θ)/(cos θ))

(Usually in and equation a/b=a, b doesn't have to be 1 when a is 0, but cos θ = 1 if and only if sin θ = 0)

The angles that satisfy cos θ = 1 is 2n(pi) (or 360n in degrees)

When n is an integer.

But if sin θ = tan θ = θ, the only answer is θ = 0.

Because sin 0 is 0 and cos 0 is 1 and tan 0 is 0

The only answer would be when θ = 0.

Thanks to the pre-existing addition and subtraction theorums, we can establish the identity:
sin(a+b) = sin(a)cos(b)+sin(a)cos(b)

Then, solving this, we get
sin(a+b) = 2(sin(a)cos(b))
sin(a)cos(b) = sin(a+b)/2

a=b, so
sin(a)cos(a) = sin(a+a)/2
sin(a)cos(a) = sin(2a)/2
Therefore, the answer is sin(2a)/2.

Let the function be f(x) = 1/(x-1)

The domain is all allowable values for which the function can be defined.

Here, except 1, any number would give the function a meaningful value. If x=1, the denominator becomes 0 and the function becomes undefined. Therefore, the domain is all real numbers except 1.

The range is all values assumed by the function.

Here, the range is negative infinity to plus infinity (that is , all real numbers).

Acute angles (less than 90 degrees)

Obtuse angles (greater than 90 degrees)

Right angles ( equal to 90 degrees)

height = 15 ft

base = 20 ft

angle of elevation = arctan (15/20) = 36.87 degrees

5

T + 5 + 3T = 1

Simplify the terms, T and 3T (think 1 apple plus 3 apples)

4T + 5 = 1

Subtract 5 from both sides.

4T = -4

then divide both sides by 4 to get T by itself.

T = -4/4

T = -1

To check, substitute T = -1 wherever you see T in your original equation.

T + 5 + 3T = 1

(-1) + 5 + 3(-1) = 1

4 - 3 = 1

1 = 1 (check)

From Greek.Trigon comes from 3-sided figure, now known as a triangle.

Metry comes from measurement.

The question does not specify the starting point.

the angle between the two sides is used in the formula A = 1/2 a*b*sin(C) where A is area, a and b are side lengths, and C is the angle between sides. Simply use algebra to rearrange the formula to solve for C.

It is the square root of: (x1-x2)2+(y1-y2)2