Trigonometry

In both radians and degrees cos(0) = 1.

It depends if you want the answer in radians or degrees.

Either way, the answer is -0.984807753 degrees or -0.3056143889 radians.

Cotangent(0.675 radians) = 84.88 approx.

Short answer, yes.

Long answer, a triangular prism has two triangular faces, its bases, and three rectangular faces, its sides, which connect the two faces. Unfolding the prism into a net reveals a rectangle divided into three rectangular sections (these are the three rectangular faces) and two congruent triangles attached along a common edge to one of these rectangles (these are the two triangular faces).

tan114 = - 2.24604. This could easily be found by inputting the degree value into a calculator!

sin^5 2x = 1/8 sin2x (cos(8x) - 4 cos(4x)+3)

Neither.

Yes.

It is a reflex angle

5 cycles.

x*pi / 180

-420*3.14 / 180 = -7.33

• No. Cosine, along with sec, is an even function. The odd functions are sin, tan, csc, and cot. The reason for this is because is you take the opposite of the y-value for the cosine function, the overall value of the function is not affected.
• Take, for example, cos(60 degrees), which equals POSITIVE 1/2.
• If you flip it over the x-axis, making the y's negative, it becomes cos(-60 degrees), or cos(300 degrees). This equals POSITIVE 1/2.
• Now let's look at an odd function. For example, sin(30 degrees) equals POSITIVE 1/2. Now take the opposite of this.
• sin(-30 degrees), or sin(330 degrees), equals NEGATIVE 1/2. This is because it is found in the fourth quadrant, where the y's are negative. Sine of theta, by definition, is y divided by r. If y is negative, sine is negative.

1 + cot2x = csc2x

The six main trigonometric functions are

sin(x)=opposite/hypotenuse

cos(x)=adjacent/hypotenuse

tan(x)=opposite/adjacent

csc(x)=hypotenuse/opposite

cot(x)=adjacent/opposite

sec(x)=hypotenuse/adjacent

Where hypotenuse, opposite, and adjacent correspond to the three sides of a right triangle and x corresponds to an angle in that right triangle.

Angle of elevation: tangent angle = opposite/adjacent and by rearranging the given formula will help to solve the problem

29.36 degrees. tan-1(45/80) = 29.36

It is 45 + 360*k deg or 135 + 360*k degrees where k is an integer.

Octant

The obvious answer is to impart a sound knowledge of the subject in the students. However, you probably want to know why anyone wants to learn trigonometry. The answer to that is this.

Trigonometry is a mathematical tool which is almost essential to know if you want to understand how to build structures cheaply and effectively. With trig. it's easy to figure out where things are most likely to break and how thick structural parts must be to carry loads safely. Trig. is also very useful to understand waves - all sorts of waves such as radio waves and waves on water.

Without trig. engineers would waste so much time trying to work things out that they'd never succeed in any job.

0.96593 (rounded)

45 degrees (+/- 180k degrees for any integer k)

or pi/4 radians (+/- pi*k radians for any integer k).

Yes.

Rather a convoluted way of saying it, but it is true.

It helps to convert this kind of equation into one that has only sines and cosines, by using the basic definitions of the other functions in terms of sines and cosines.

sin x / (1 - cos x) = csc x + cot x

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

Now it should be easy to do some simplifications:

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

Multiply both sides by 1 + cos x:

sin x (1 + cos) / ((1 - cos x)(1 + cos x)) = (1 + cos x)2 / sin x

sin x (1 + cos) / (1 - cos2x) = (1 + cos x)2 / sin x

sin x (1 + cos) / sin2x = (1 + cos x)2 / sin x

sin x (1 + cos x) / sin x = (1 + cos x)2

1 + cos x = (1 + cos x)2

1 = 1 + cos x

cos x = 0

So, cos x can be pi/2, 3 pi / 2, etc.

In some of the simplifications, I divided by a factor that might be equal to zero; this has to be considered separately. For example, what if sin x = 0? Check whether this is a solution to the original equation.