Trigonometry

nah

You use the arcsine or sin-1 function. For any value of sin(X), the function will return a value for the angle in the range [-pi/2, pi/2]. There are, however, infinitely many angles which will have the same value for sine. They are

X + 2k*pi and (2k+1)*pi - X radians where k is any integer.

If you still work with degrees, the answers are

X + 360k and (2k+1)*180 - X degrees.

It is infinite, in both directions. But it can be restricted to a smaller interval.

tan(3x)=1

3x= PI/4

x=PI/12 is the smallest positive number

10 * sine(9) = 1.5643

A stack of this height could be made with 1.000, .350, .114 and .1003 blocks for the minumum number of blocks.

26 = 64

There are 2 cups in a pint. There are 2 pints in a quart. There are 4 pints in a half gallon, like if you bought a half a gallon if milk at a store. There are 8 pints in a gallon.

10 pints equals 20 cups.

10 pints equals 5 quarts

10 pints equals 2 and a half gallons.

10 pints equals 1 and a quarter gallons.

Hope I helped!

When none of the angles are known, and using Pythagoras, the triangle is known not to be right angled.

cos(75 deg) = 0.2588, approx.

assuming that you mean what is theta if sin 4 theta = 0 then then theta=0, 0.25pi, 0.5pi, 0.75pi...

if not then without additional information the best answer you can get is sin4theta=sin4theta

1 knot = 1 nautocal mile per hour.

So 428 nm @ 20 knots per hour will take 428/20 = 21.4 hours.

After 12 hours, it is 20*12 = 240 nautical miles away.

Its distance East is 240*cos(1.4deg) = 239.9 nautical miles and

its distance South is 240*sin(1.4deg) = 5.9 nautical miles.

By the sine rule,

sin(C)/c = sin(B)/b

so sin(C) = 25/15*sin(32d15m) = 0.8894

so C = 62.8 deg or 117.2 deg.

Therefore, A = 180 - (B+C) = 85.0 deg or 30.5 deg

and then, using the sine rule again,

a/sin(A) = b/sin(B)

so a = sin(A)*b/sin(B) = 28 or a = 14.3

sin(30) = sin(90 - 60) = sin(90)*cos(60) - cos(90)*sin(60)

= 1*cos(60) - 0*sin(60) = cos(60).

-2(cot2theta)

The cosine of 10 degrees is 0.98480775301221. Hope I helped!

cosine = adjacent/hypotenuse

Period is how long it takes for the sine and cosine functions to restart repeating themselves. Both have a period of 2pi (360 degrees).

The cosine of 70 degrees is 0.34202014332567.

the answer is (area)

2.41

(40000000 x .00002)=800

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.

sin-1 (0.91) = about 1.14328 radians.

If you have the sine of an angle and you need to find the angle, you have a

few choices. They're exactly the same choices that you have if you're going

the other way ... you have the angle and you need to find its sine:

-- pocket calculator, or computer . . . the way it's most often done these days

-- look it up in a table in a reference book

-- calculate it on paper from an infinite series . . . technically possible, but no reason

to subject yourself to the heartburn unless you need extreme precision, better than

what you can get with a 10-digit calculator.

Let 'theta' = A [as 'A' is easier to type]

sec A - 1/(sec A)

= 1/(cos A) - cos A

= (1 - cos^2 A)/(cos A)

= (sin^2 A)/(cos A)

= (tan A)*(sin A)

Then you can swap back the 'A' with theta