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it depends...
- theta:
theta is usually the letter given to any angle in the triangle (the letter theta is from the greek alphabet). usually in trigonometry you would use it when using SOHCAHTOA (sin=opposite/hypotenuse; cos=adjacent/hypotenuse; tan=opposite/adjacent) e.g. the sun is at an angle of 30°. if the shadow's length is 40m, find the length of the flagpole.
tan30=h/40
tanθ=opp/adj
40xtan30=h
h=23.09m
-'opposite' (opp)is the opposite side from the angle you are trying to find out
-'adjacent' (adj)is the side next to the angle you are trying to find out
-'hypotenuse' (hyp)is also next to the angle you are trying to find out, but it is also opposite the right angle and it is the longest side
- x:
'x' is usually used to represent a length (either the base, height or hypotenuse). using SOHCAHTOA it would be either the opposite, adjacent or hypotenuse. using the example above x could substitute h
the difference is that theta is used for the angles and x is for the other measurements(length or distance). i don't think that there similar but thats just me...
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What is 4sin theta cos theta?
by using x instead of theta (to make it easier to type), 4sinxcosx can be simplified to 2sin2x.
Verify that Cos theta cot theta plus sin theta equals csc theta?
It's easiest to show all of the work (explanations/identities), and x represents theta. cosxcotx + sinx = cscx cosx times cosx/sinx + sinx = csc x (Quotient Identity) cosx2 /sinx + sinx = csc x (multiplied) 1-sinx2/sinx + sinx = csc x (Pythagorean Identity) 1/sinx - sinx2/sinx + sinx = csc x (seperate fraction) 1/sinx -sinx + sinx = csc x (canceled) 1/sinx = csc x (cancelled) csc x =csc x (Reciprocal Identity)
Why does sin theta squared plus cos theta squared equal 1?
Sin2(theta) + cos2(theta) = 1 for the same reason that the sides of a right triangle squared equal the hypotenuse squared - The pythagorean theorem.In the unit circle (origin = (0,0), radius = 1), an angle theta is the angle made by some arbitrary ray drawn from the origin at an angle relative to the x axis. The point of that ray that intersects with the circle is the point (x,y).Sin(theta) is defined as x, and cos(theta) is defined as y. These are primary trigonometric identities, which link trigonometry with geometry.Since the points (0,0) (x,0) (x,y) (0,x) describe a right triangle, with (0,x) (0,0) (x,0) being the right angle, then x2 + y2 = 12, or sin2(theta) + cos2(theta) = 1.If this is not clear, draw a circle around the origin, draw a line from the center to an arbitrary point on the circle, and draw the x and y perpendiculars of that point to each axis. You will see a right triangle. X is sine, Y is cosine, and 1 is hypotenuse. It does not matter if X and/or Y is negative - the squaring will make it positive - and the pythagorean theorem should be visible.
How do you solve tan squared theta - tan theta equals 0?
Let x = theta, since it's easier to type, and is essentially the same variable. Since tan^2(x)=tan(x), you know that tan(x) must either be 1 or zero for this statement to be true. So let tan(x)=0, and solve on your calculator by taking the inverse. Similarly for, tan(x)=1
How do you simplify cot of theta times sin of theta?
By converting everything to sines and cosines. Since tan x = sin x / cos x, in the cotangent, which is the reciprocal of the tangent: cot x = cos x / sin x. You can replace any other variable (like thetha) for the angle.
What is the significance of the x-value in a sine wave function?
The answer will depend on where, in the sine function, the x-value appears: For example, its roles in f(x) = sin(x), or f(x, theta) = x*sin(theta) or f(x, theta) = sin(x*theta) f(theta) = sin(theta + x) are quite different.
How do you solve for x and y in an angle?
If X and Y are sides of a right triangle, R is the hypoteneuse, and theta is the angle at the X-R vertex, then sin(theta) is Y / R and cosine(theta) is X / R. It follows, then, that X is R cosine(theta) and Y is R sin(theta)
How do you get the csc theta given tan theta in quadrant 1?
If tan(theta) = x then sin(theta) = x/(sqrt(x2 + 1) so that csc(theta) = [(sqrt(x2 + 1)]/x = sqrt(1 + 1/x2)
When is tan theta theta?
tan (theta x theta) : must square the value of the angle, theta, before applying the trig function, tangent.
How do you transfer spherical coordinate into cartesian and vice versa?
If spherical coords are r and theta, then x = r*cos(theta) and y = r*sin(theta) Conversely, r = sqrt(x2 + y2) and theta = arctan(y/x) provided x is not zero. and theta = 90 deg when x = 0
What is 4sin theta cos theta?
by using x instead of theta (to make it easier to type), 4sinxcosx can be simplified to 2sin2x.
In trig how is the value of r interpreted geometrically in the definitions of the sine cosine secant and cosecant?
In trigonometry, the value of R is the radius of the circle, and is usually normalized to a value of 1. If the circle is at the X-Y origin, and theta is the angle between the radius line R, and X and Y are the X and Y coordinates of the point on the circle at the radius line, then... sine(theta) = Y / R cosine(theta) = X / R secant(theta) = 1 / cosine(theta) = R / X cosecant(theta) = 1 / sine(theta) = R / Y
Why is 2 sin theta cos theta equal to sin 2theta?
because sin(2x) = 2sin(x)cos(x)
How do you simplify csc theta minus cot x theta times cos theta plus 1?
There can be no significant simplicfication if some of the angles are theta and others are x, so assume that all angles are x. [csc(x) - cot(x)]*[cos(x) + 1] =[1/sin(x) - cos(x)/sin(x)]*[cos(x) + 1] =1/sin(x)*[1 - cos(x)]*[cos(x) + 1] =1/sin(x)*[1 - cos2(x)] =1/sin(x)*[sin2(x)] = sin(x)
Examples of the three basic trigonometric ratios?
Given a unit circle (radius = 1) and a counterclockwise angle (theta) between the positive x axis, with the x-y coordinate of the point on the circle that the angle intersects, the three basic trigonometric ratios are... 1. sine (theta) is y 2. cosine (theta) is x 3. tangent (theta) is x / y
How do you find theta if 2sin theta plus 1 equals 0 and 0 is less than or equal to theta which is less than 2pi?
2 sin(x) + 1 = 0 2 sin(x) = -1 sin(x) = -1/2 x = 210° and 330°
Why tan theta sin theta divided by cos theta?
The answer depends on how the ratios are defined. In some cases tan is DEFINED as the ratio of sine and cosine rather than from the angle in a right angled triangle.If the trig ratios were defined in terms of a right angled triangle, thensine is the ratio of the opposite side to the hypotenuse,cosine is the ratio of the adjacent side to the hypotenuse,and tangent is the ratio of the opposite side to the adjacent side.It is then easy to see that sin/cos = (opp/hyp)/(adj/hyp) = opp/adj = tan.If sine and cosine are defined as infinite sums for angles measured in radians, iesin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...andcos = 1 - x^2/2! + x^4/4! - x^6/6! + ...then it is less easy to see tan = sin/cos.
