Question

easy way to learn trigonometrical ratios of standard angles

Answer 1

Create a table. In the first row, write down the trigonometric ratios (sin, cos, tan, cot). In the first column, write down the angles (0°, 30°, 45°, 60°, 90°). Leave other entries blank.2Fill in the sine column. We will fill in the blank entries in the sin column using the expression √x/2. Once the sine column is filled, we'll be able to fill all other columns effortlessly!For the 1st entry in the sine column (that is, sin 0°), set x = 0 and plug it in the expression √x/2. Thus, sin 0° = √0/2 = 0/2 = 0For the 2nd entry in the sine column (that is, sin 30°), set x = 1 and plug it in the expression √x/2. Thus, sin 30° = √1/2 = 1/2For the 3rd entry in the sine column (that is, sin 45°), set x = 2 and plug it in the expression √x/2. Thus, sin 45° = √2/2 = 1/√2For the 4th entry in the sine column (that is, sin 60°), set x = 3 and plug it in the expression √x/2. Thus, sin 60° = √3/2.For the 5th entry in the sin column (that is, sin 90°), set x = 4 and plug it in the expression √x/2. Thus, sin 90° = √4/2 = 2/2 = 1.3Fill in the cosine column. Simply copy the entries in the sine column in reverse order into the cosine column. This is valid because sin x° = cos (90-x)° for any x.4Fill in the tangent column. We know that tan = sin / cos. So, for every angle take its sin value and divide it by the cos value to get the corresponding tan value. For example, tan 30° = sin 30° / cos 30° = (√1/2) / (√3/2) = 1/√35Fill in the cotangent column. Simply copy the entries in tangent column in reverse order into the cot column. This is valid because tan x° = sin x° / cos x° = cos (90-x)° / sin (90-x)° = cot (90-x)° for any x.Community Q&AHow do I write sec and co-sec values?wikiHow ContributorValues of cosec, sec and cot can be found by taking inverse of sin, cos and tan respectively for the given angle.Not Helpful 68 Helpful 234Why tan 90 degree is not defined?wikiHow ContributorThe sine of 90° equals 1, and the cosine of 90° equals zero. It happens that the tangent of any angle is equal to its sine divided by its cosine. Thus, the tangent of 90° equals 1 divided by zero. However, dividing by zero is "undefined," because it equals infinity (which is not a defined number). That makes the tangent of 90° undefined.Not Helpful 32 Helpful 94How do I fill a cosec and sec value?wikiHow ContributorYou can reverse the numerator and denominator of sin to find cosec like (30°= 0= 1/0 i.e., not defined) and of cos to find sec.Not Helpful 27 Helpful 65Where can I find the cos when I know the sin and the location of theta?wikiHow ContributorDraw the polar triangle with the theta value and the two sides given by sin. They should be given to you in the form of a fraction, sin=opposite/hypotenuse. Then, use the Pythagorean theorem to solve for the third side and do cos=adjacent/hypotenuse.Not Helpful 48 Helpful 90How do I use cos in trigonometry to find an angle?DonaganCalculate the ratio between the adjacent side and the hypotenuse, then look up that ratio in a cosine table, which will tell you the angle.Not Helpful 17 Helpful 36How can all the trigonometry identities be learned the fastest?DonaganIt's a simple matter of memorization.Not Helpful 25 Helpful 47How do I use tan in trig to find an angle?wikiHow Contributortan(x)=sin(x)/cos(x)Not Helpful 22 Helpful 40How can I remember angles exceeding 90 degrees?wikiHow ContributorGraph the equations, sin(x), cos(x), tan(x), csc(x), sec(x), and cot(x). Use the x coordinates 0, 90, 180, 270, and 360 to see how each trigonometric function flows on the graph.Not Helpful 34 Helpful 57Where is sec and cosec?DonaganThe author of this article chose not to display those functions. They're easily found, however: the secant of an angle is the reciprocal of its cosine, and the cosecant of an angle is the reciprocal of its sine.Not Helpful 14 Helpful 26How can I know the angles exceeding 180?wikiHow ContributorYou have to learn the quadrant system of trigonometric ratios.Not Helpful 0 Helpful 2Show more answersUnanswered QuestionsHow can I know angle is exceeding 180 degrees?Answer this question Flag as...What is the symbol for not defined?Answer this question Flag as...In 2 step while finding sin 45 it is given 2/2=1/2. How it is solved?Answer this question Flag as...How can I know angle is exceeding 180 degrees?Answer this question Flag as...Show more unanswered questionsAsk a QuestionSubmitVideoTipsDo not leave irrational numbers in the denominator. For example, tan30° = 1/√3. Don't leave it that way. Instead, write it like √3/3.WarningsYou can't divide by 0! tan90° = ±∞ and cot0° = ±∞, but ∞ isn't considered an actual number, so don't write it. Write "not defined" or "n/a" (not applicable) instead.EditRelated wikiHowsHow toSolve Trigonometric EquationsHow toSolve Trigonometric InequalitiesHow toArrive at ‐1 and 1 from Spaces or ZeroesHow toCreate Method 1 Sine Waves on CylindersHow toCreate a Spirallic Spin Particle Path or Necklace Form or Spherical Bord