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Trigonometry
Trigonometry is a field of mathematics. It is the study of triangles. Trigonometry includes planar trigonometry, spherical trigonometry, finding unknown values in triangles, trigonometric functions, and trigonometric function graphs.
3,810 Questions
What solid shapes can both roll and slide?
cylinders: slide on the small sides, roll on the round one
The length of an arc on a circle of radius 16, with an arc angle of 60 degrees is about 16.8.
The circumference of the circle is 2 pi r, or about 100.5. 60 degrees of a circle is one sixth of the circle, so the arc is one sixth of 100.5, or 16.8.
Is sine of an angle directly proportional to an angle?
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)]
What is another name for a cartesian coordinate system?
It is the Cartesian plane or grid system whereas coordinates of x and y are plotted on it.
The area of a triangle with two sides equal to 1 foot and the angle between those two sides equal to 45 degrees is 0.354 square feet.
Draw a triangle, one side of length 1, from the origin to the right along the x axis. The second side, also of length 1, goes up and to the right from the origin at an angle of 45 degrees with respect to the x axis. The third side connects the two end points of those line, but the length of that line does not matter.
Draw a fourth line from the top of the triangle straight down to the x axis. That is the height of the triangle, and it is also sine(45 degrees), which is one half the square root of two or 0.707. Take the base (1), multiply by the height (0.707) and divide by 2 and you get 0.354.
Technically, the fourth line is sine(45 degrees) divided by the hypotenuse, but since the hypotenuse is 1 (the second line), it was omitted in the prior paragraph for clarity.
What does trigonometry involve?
You need to be able to solve logarithms and be very good at algebra. In college, you have to be able to do college level algebra before you can take trig.
How are sine and cosine and secant related?
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.
How do you find x assume that segments that appear tangent are tangent?
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.
13 feet
i34 is the complex part of the number 0+i34. The real part is 0, so this is a purely imaginary number.
The length, or magnetude, of the vector is the square root of (6^2 + 8^2), or 10. The angle of inclination is tan-1 of (8/6), or 53.13 degrees.
Why does the sine graph always start at 0?
sin(0) = 0 but, in general, the sine graph need not start at 0.
For example, sin(x + 2) does not start at 0.
How do you determine the sign of a sine curve?
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.
What ratio correctly describes the cosine function?
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.
A ladder 10 ft long leaning against a wall at a 71 angle how high up the wall does the ladder reach?
10 sin71 = 10 x 0.9455 = 9.455 feet (just under 9' 5½")
The given angle is 1291 degrees what terminal quadrant does it lie in?
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).
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)
