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Using exact values find the numerical value of sin 30 degrees cos 240 degrees plus sin 210 degrees sin 300 degrees?
SQRT(3)/4 - 1/4
How do you graph a function in trigonometry?
y = sin x, or y = cos x etc. can be graphed by making a table of values. The x column in the table would be angle measurements (usually in degrees or radians) and the y column would be the trig. function value. Then plot the points and sketch the curve going thru those points. Ex: for y = sin x x , y 0 0 30 0.5 45 0.707 etc and then graph these
Is all sin equal?
yeah. a sin is still a sin.
What is the value of sin 40 degrees?
It is:- sin(40) = 0.6427876097
What is the value of sin of 62 degrees?
It is: sin(62) = 0.8829475929.
Using exact values find the numerical value of sin 30 degrees cos 240 degrees plus sin 210 degrees sin 300 degrees?
SQRT(3)/4 - 1/4
Is the cosine sine and tangent of an angle equal to each other?
No; those could be three different values, or sometimes two of them might be the same. For example, if the angle is 45 degrees, the values are about... cos:0.707 sin: 0.707 tan: 1 For 45 degrees, the cosine and sine are the same. For 36 degrees, cos:0.809 sin: 0.588 tan: .727
Can you transform sine functions into cosine functions?
If you know the measure of one angle, and the length of one side of a triangle, you can find the measures of the other sides and angles. From there, you can find the values of the other trig functions. cos (x) = sin (90-x) in degrees there are other identities such as cos^2+sin^2=1, so cos^2=1-sin^2
What trigonometric value is equal to cos 62?
The solution is found by applying the definition of complementary trig functions: Cos (&Theta) = sin (90°-&Theta) cos (62°) = sin (90°-62°) Therefore the solution is sin 28°.
What is the co-function of sin 19 degrees?
cos 71
What is value of sin theta when theta equal to 13.9222?
answer is 2.34 degrees answer is 2.34 degrees
What are the ways on how to solve trigonometric equations?
Generalities.A trig equation contains one or many trig functions of the variable arc x. Solving for x means finding the values of the trig arcs x whose trig functions make the equations true.Example of trig equations:sin (x + Pi/3) = 0.75 ; sin 2x + cos x = 1 ; tan x + 2 cot x = 3 ; tan x + cot x = 1.732.sin x + sin 3x = 1. 5 ; sin x + sin 2x + sin 3x = cos x + cos 2x + cos 3x ;The answers, or values of the solution arcs x, are expressed in terms of radians or degrees:x = Pi/3 ; x = 137 deg. ; x = 2Pi/3 + 2k.Pi ; x = - 17. 23 deg. ; x = 360 deg.The Trig Unit CircleIt is a circle with radius R = 1 unity, and with an origin O. This unit circle defines all trig functions of the variable arc x that rotates counterclockwise on it.When the arc AM, with value x, rotates on the unit circle,The horizontal axis OAx defines the trig function f(x) = cos x.The vertical axis OBy defines the trig function f(x) = sin x.The vertical axis AT defines the trig function f(x) = tan x.The horizontal axis BU defines the trig function f(x) = cot xThe trig unit circle will be used as proofs for solving basic trig equations and trig inequalities.The periodic property of all trig functions.All trig functions are periodic meaning they come back to the same values when the arc x completes one period of rotation on the trig unit circle.Examples:The trig functions f(x) = sin x and f(x) = cos x have 2Pi as periodThe trig function f(x) = tan x and f(x) = cot x have Pi as period.Find the arcs whose trig functions are known.You must know how to find the values of the arcs when their trig functions are known. Conversion values are given by calculators or trig tables.Example: After solving, you get cos x = 0.732. Calculators (or trig table) gives x = 42.95 deg.. The Unit Circle will give an infinity of other arcs x that have the same cos value. These values are called extended answers.Example: Get sin x = 0.5. Trig table gives x = Pi/6. The unit circle give an infinity of extended answers.Concept for solving trig equations.To solve a trig equations, transform it into one or many basic trig equations.Basic trig equations.There are 4 of them. They are also called "trig equations in simplest form".sin x = a ; cos x = a (a is a given number)tan x = a ; cot x = aSolving basic trig equations.The solving method proceeds by considering the various positions of the variable arc x, rotating on the trig circle, and by using calculators (or trig tables).Example 1. Solve sin x = 0.866Solution. There are 2 answers given by calculators and the trig circle:x = Pi/3 ; x = 2Pi/3 (answers)x = Pi/3 + 2k.Pi ; x = 2Pi/3 + 2k.Pi (extended answers)Example 2. Solve cos x = 0.5Solution. 2 answers given by the trig table and the trig circle:x = 2Pi/3 ; x = - 2Pi/3 (answers)x = 2Pi/3 + 2k.Pi ; x = -2Pi/3 + 2k.Pi (extended answers)Note. The answer x = - 2Pi/3 can be replaced by x = 2Pi - 2Pi/3 = 4Pi/3.How to transform a given trig equation into basic trig equations.You may use:- common algebraic transformations, such as factoring, common factor, polynomials identities....- definitions and properties of trig functions...- trig identities (the most needed)Common Trig Identities.There are about 31 of them. Among them, the last 14 identities, from #19 to #31, are called "Transformation Identities" since they are necessary tools to transform a given trig equation into many basic ones. See book titled "Solving trig equations and inequalities" (Amazon e-book 2010)Examples of trig identities: sin^2 a + co^2 a = 1 ; sin 2a = 2sin a.cos a ;1 - cos 2a = 2 sin^2 a ; cos a = (1 - t^2)/(1 + t^2)Methods to solve trig equations.There are 2 common methods to solve a trig equation, depending on transformation possibilities.Method 1. Transform it into a product of many basic trig equations, by usingcommon transformation tools or by using trig identities.Example 3. Solve 2cos x + sin 2x = 0.Solution. Replace sin 2x by 2sin x.cos x (Trig Identity #10)2cos x + sin 2x = 2cos x + 2sin x.cos x = 2cos x(1 + sin x).Next, solve the 2 basic trig equations: cos x = 0 and sin x + 1 = 0.Example 4. Solve cos x + cos 2x + cos 3x = 0.Solution. Using trig identity #26, transform it into a product of 2 basic trig equations: cos 2x (2 cos x + 1) = 0. Next, solve the 2 basic trig equations: cos 2x = 0 and cos x = -1/2.Method 2. If the trig equation contains many trig functions, transform it into an equation that contains only one trig function as a variable.Example 5. Solve 3cos ^2 x - 2sin^2 x = 1 - 3sin xTransform the equation into the one containing only sin x. Replace cos^2 x = 1 - sin^2 x (Trig Identity 1). Call sin x = t.3(1 - sin^2 x) - 2sin^2x +3sin x - 1 = 03 - 3t^2 - 2t^2 + 3t - 1 = -5t^2 + 3t + 2 = 0.This is a quadratic equation with 2 real roots 1 and -2/5. Next solve the 2 trig basic equations: sin x = t = 1 and sin x = t = -2/5.The common period of a trig equation.The common period of a given trig equation must equal the least multiple of all the contained trig functions' periods.Example: The equation cos x + tan x = 1 has 2Pi as common period.The equation f(x) = sin 2x + cos x = 0 has 2Pi as common periodThe equation sin x + cos x/2 has 4 Pi as common period.Unless specified, a trig equation must be solved covering at least one common period.Solving special types of trig equations.There are a few special types of trig equations that require specific transformations.Examples: asin x + bcox x = ca(sin x + cos x) +bsin x.cos x = casin^2 x + bsin x.cos x + c cos^2 x = 0.Checking answers.Solving trig equation is a tricky work that easily leads to errors and mistakes. The answers should be carefully checked.After solving, you may check the answers by using graphing calculators. To know how, see the book mentioned above.(This article was written by Nghi H. Nguyen, the co-author of the new Diagonal Sum Method for solving quadratic equations)
Sine divided by cosine?
Trig identity... sin/cos = tangent
What is the exact values of sin 2 pi?
2*pi is one complete revolution, i.e. 360 degrees. Sin of 2*pi = sin 360º = 0
How do you find C from sin C equals 0.3328 using a calculator?
( are you in radians, or degree mode? will do both) Radians: sin C = 0.3328 arcsin(0.3328) = C =0.3393 radians --------------------- Degrees: sin C = 0.3328 arcsin(0.3328) = 19.44 degrees ------------------------- arcsin is a secondary function on most calculators and you should recognize the algebraic/trig manipulations.
Why does x equal 0 when finding the sin of 90 degrees?
On the unit circle sin(90) degrees is at Y = 1 and as that is on the Y axis X will equal = 0. Ask yourself. Where would 90 degrees be on a 360 degree circle? Straight up.
How is it possible to know all of the values of the unit circle by only knowing the values of sinx cosx and tanx of quadrant 1 angles and those on the axes?
Each angle may be used as a 'reference angle'. A 30 deg. angle in QI will have a sides, x = (sq rt 3)/2 , y= 1/2, r = 1. An angle of 150 deg (180 - 30) will create a triangle in Q2 with the same lengths except x is now negative. So if you know all trig values for 30, then change the signs for cos and tan because x is now negative and you know the values of all. Similarly for 210 deg (180+30) creates the same triangle in Q3 but both x and y values are neg. Sin and cos are neg, but tan (divide 2 neg's) is positive. In Q4 (360 - 30) creates a 330 deg angle for a triangle that is the same shape, but y is neg and x is pos so that sin and tan are neg but cos is pos. ex: sin 30 = 1/2 (Q1), sin 150 = -1/2 (Q2), sin 210 = -1/2 (Q3), sin 330 = 1/2 (Q4) notice only the sign (+/-) changes. Most trig classes teach you that Q1 all trig functions are pos, Q2 sin is pos, Q3 tan is pos, Q4 cos is pos. Remember this and the 1st Quadrant values and then you can get all trig functions using the concept of a reference angle.
