Trigonometry

No. The sine of an angle is not directly proportional to the angle. It is a function of the angle, but it is periodic, repeating every 360 degrees of the angle.

cos(195) = cos(180 + 15) = cos(180)*cos(15) - sin(180)*sin(15)

= -1*cos(15) - 0*sim(15) = -cos(15)

= -cos(60 - 45)

= -[cos(60)*cos(45) + sin(60)*sin(45)]

= -(1/2)*sqrt(2)/2 - sqrt(3)/2*sqrt(2)/2

= - 1/4*sqrt(2)*(1 + sqrt3) or -1/4*[sqrt(2) + sqrt(6)]

It's 1/2 of sin(2 theta) .

sin(0) = 0 but, in general, the sine graph need not start at 0.

For example, sin(x + 2) does not start at 0.

Trigonometry is used effectively in electronics.

Yes, they can exist.

Thousands, if not more.

There are all sorts of musical instruments.

There are instruments for performing many different tasks.

Then there are instruments for measuring all sorts of physical, chemical properties of things.

A tangent refers to the way in which a curve is measured. The amount of deviation from the segment line is measures, then a formula applied to find the tangent.

-1<cosine<1

Sine and cosine are cofunctions, which means that their angles are complementary. Consequently, sin (90° - x) = cos x. Secant is the reciprocal of cosine so that sec x = 1/(cos x). Knowing these properties of trigonometric functions, among others, will really help you in other advance math courses.

10 sin71 = 10 x 0.9455 = 9.455 feet (just under 9' 5½")

3rd quadrant. The four 90 degree quadrants together formed 360 degrees. When a given angle is greater than 360 degrees, subtract 360 from it till a value smaller than 360 is obtained. In this way, we can determine the quadrant in which the given angle lies. Here the final angle obtained is 211 degrees (1291-3x360=211).

The sine of 22.5 degrees is 0.383

Cosine(42 radians) = -0.399985

Cosine(42 degrees) = 0.743146

For 0 < x < pi. sin(x) is positive,for pi < x < 2*pi, sin(x) is negative

and these intervals can be left or right-shifted by any multiple of 2*pi radians.

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x = (2n+1)*pi/2 radians for any integer n.

It is -sqrt(1 + cot^2 theta)

0 degree to 90 degrees.

The cosine of theta is adjacent over hypotenuse, given a right triangle, theta not being the 90 degree angle, adjacent not being the hypotenuse, and theta being the angle between adjacent and hypotenuse.

In a unit triangle, i.e. in a unit circle circumscribed with radius one, and theta and the center of the circle at the origin, cosine of theta is X.

Arthur Pythagoras rules! 12 x 12 = 3 x 3 + x2, so x2 = 144 - 9 and x = sqrt 135 = 11.62 so to the nearest foot it reaches 12 feet (actually 11.62)

90 degrees

YES! If you can't do algebra, you won't last ten seconds in trigonometry. It basically is algebra, just using equations within equations.

False.

It too will have a value of 5