Trigonometry

Yes, it can.

If you plot theta and sin(theta) on the same graph, you will see where they intersect.

I do not know of an analytical expression for this point; I think only numerical results are possible.

sec + tan = cos /(1 + sin)

sec and tan are defined so cos is non-zero.

1/cos + sin/cos = cos/(1 + sin)

(1 + sin)/cos = cos/(1 + sin)

cross-multiplying, (1 + sin)2 = cos2

(1 + sin)2 = 1 - sin2

1 + 2sin + sin2 = 1 - sin2

2sin2 + 2sin = 0

sin2 + sin = 0

sin(sin + 1) = 0

so sin = 0 or sin = -1

But sin = -1 implies that cos = 0 and cos is non-zero.

Therefore sin = 0 or the solutions are k*pi radians where k is an integer.

Consider any triangle ABC, and let AD be the altitude from A on to BC.

Then sin(B) = AD/AB so that AD = AB*sin(B)

and sin(C) = AD/AC so that AD = AC*sin(C)

Therefore AB*sin(B) = AC*sin(C)

or c*sin(B) = b*sin(C) where the lower case letter represents the side opposite the angle with the upper case name.

Divide both sides by bc to give sin(B)/b = sin(C)/c.

Similarly, using the altitude from B you can show that sin(A)/a = sin(C)/c.

Combining with the previous result,

sin(A)/a = sin(B)/b = sin(C)/c.

It is a non-linear function of theta.

sin[cos-1(x)] is an expression; it is not an equation (nor inequality). An expression cannot be solved.

Any number can be a tan. So -sqrt(17), 19.56, 45678942 are all examples of tan.

Cosine can have any value in the range [-1, 1].

No.

Yes

1 and the positive and negative square roots of 2

y-axis

1000 1000

sin(39 deg) = 0.6293

128484

The name originated in Wales during the mid 1200's and was mostly 'transported' over to Ireland during the 1600's. In 1842, The first Irishmen with the surname Lattimore moved over to England in the attempt for work during the Industrial Revolution. Ever since then, the surname Lattimore has been mostly common in England, Ireland and Wales.

Fertilizers typically add nitrates, phosphates and sulfates as well as salts of magnesium, potassium and calcium. They may also contain micronutrients of other metals.

0.0348995 (rounded)

The trigonometric function of an angle gives a certain value

The arc trigonometric function of value is simply the angle

For example, if sin (30 degrees) = 0.500

then arc sine ( 0.500) = 30 degrees

The cotangent of 60 degrees is 1\(3^1\2).

x = 1.088348752

A circle is a shape with a circumference of 360 degrees.

1/3 pi times r2 times height

that's the closest I could get on this thing

They are ued all over the place for Ex. TV, oven, shelves, pizza, windows, mirrors, shoeboxes, and amything else like that.

If the pole is on level ground then you have the outline of a right angled triangle with an opposite side of 3 feet and an adjacent angle of 30 degrees. To find the length of the adjacent side (which in effect is the shadow of the pole) use the tangent ratio: tangent = opposite/adjacent which can be rearranged to: adjacent = opposite/tangent adjacent = 3/tangent 30o = 5.196152423 feet Therefore the shadow cast by the pole is 5.2 feet corrected to one decimal place.

It is zero.

cos(phi - 1) = cos(phi)cos(1) + sin(phi)sin(1)