Trigonometry

tan(61°) = 1.80405 (rounded)

Sin(x) cos(x) = 1/2 of sin(2x)

It is 66 deg 15 min 0 sec.

In Geometry, you learn about triangles. In Trigonometry you learn even more about triangles.

cos(195) = -0.965925826289

Sin (theta) can most easily be found on a scientific calculator. You can also approximate it with Taylor's Series...

sin(x) = SummationN=0toInfinity (-1N / (2N + 1) !) (x(2N+1)))

sin(x) = x - x3/3! + x5/5! - x7/7! + ...

Using only the four terms above, you can approximate sin(x) within about 0.000003 in the interval x = [-1, +1].

Yes, because all sound waves can be modelled as sine (or cosine) waves, or combinations of sine waves.

If sin (theta) is 3/5, then sin2 (theta) is (3/5)2, or 9/25.

cos2(theta) = 1

cos2(theta) + sin2(theta) = 1 so sin2(theta) = 0

cos(2*theta) = cos2(theta) - sin2(theta) = 1 - 0 = 1

tan(60°) = sqrt(3)

tan(-60 degrees) = - sqrt(3)

Triangles with three equal sides are called equilateral triangles.

To find the exact value of tan 105°.

First, of all, we note that

sin 105° = cos 15°; and

cos 105° = -sin 15°.

Thus, tan 105° = -cot 15° = -1 / tan 15°.

Using the formula

tan(α - β) = (tan α - tan β) / (1 + tan α tan β);

and using, also, the familiar values

tan 45° = 1, and

tan 30° = ½ / (½√3) = 1/√3 = ⅓√3;

we have,

tan 15° = (1 - ⅓√3) / (1 + ⅓√3);

whence,

cot 15° = (1 + ⅓√3) / (1 - ⅓√3)

= (√3 + 1) / (√3 - 1) {multiplying through by √3}

= (√3 + 1)2 / (√3 + 1)(√3 - 1)

= (3 + 2√3 + 1) / (3 - 1)

= (4 + 2√3) / 2

= 2 + √3.

Therefore,

tan 105° = -cot 15° = -2 - √3,

which is the result we sought.

We are asked the exact value of tan 105°, which we gave above.

We can test the above result to 9 decimal places, say, by means of a calculator:

-2 - √3 = -3.732050808; and

tan 105° = -3.732050808;

thus indicating that we have probably got the right result.

There is no way to find perimeter from a 3D figure. However, you can find the perimeter of a side of a triangular prism by using perimeter formulas for a parallelogram or triangle.

Periodically

The answer depends on whether a or c is the hypotenuse: b cannot be the hypotenuse since the hypotenuse MUST be the longest side.

Suppose a is the hypotenuse.

Then a2 = b2 + c2 = 122 + 182 = 144 + 324 = 468. So a = 21.63 inches (approx).

Suppose c is the hypotenuse.

Then c2 = b2 + a2 = 182 = 122 + a2. So a2 = 180 and a = 13.42 inches (approx).

In a trigonometric equation, you can work to find a solution set which satisfy the given equation, so that you can move terms from one side to another in order to achieve it (or as we say we operate the same things to both sides).

But in a trigonometric identity, you only can manipulate separately each side, until you can get or not the same thing to both sides, that is to conclude if the given identity is true or false.

The equations for projectiles shouldn't just have theta, they should have sin(theta) or cos(theta).

As long as you have your calculator set in the right mode, either will work when you evaluate sin or cosine.

Example: Say you have a projectile launched at 30 degrees above horizontal. In order to find the y velocity, you will have to calculate sin(30) with you calculator in degree mode. If instead you called this angle pi/6 (the same angle, just in radians), you could enter sin(pi/6) in your calculator in radians mode and get the same answer.

COS 16.5 = 0.7

As θ increases from 0 to π/2 (90o) sin θ increases until it reaches a maximum value of 1 when θ = π/2.

As θ increases from π/2 (90o) to 3π/2 (270o) sin θ decreases until it reaches a minimum value of -1 when θ = 3π/2.

As θ increases from 3π/2 (270o) to 3π (360o) sin θ increases until it reaches the value of 0 it had when θ = 0.

From this point, as θ increases (by the same amounts) sin θ repeats this same cyclic behaviour.

The cosecant of an angle is the reciprocal of the sine of that angle. So, to find the cosecant of 105 degrees, you first need to find the sine of 105 degrees. The sine of 105 degrees is approximately 0.9659. Therefore, the cosecant of 105 degrees is approximately 1.0353 (1 divided by 0.9659).

28

The Law of Sines: a/sin A = b/sin B = c/sin C

24/sin 42˚ = c/sin (180˚ - 42˚ - 87˚) since there are 180˚ in a triangle.

24/sin 42˚ = c/sin 51˚

c = 24(sin 51˚)/sin 42˚ ≈ 28

cos 71