Learn how cosecant, secant, and cotangent are the reciprocals of the basic trig ratios: sine, cosine, and tangent.
Log in Nayan Bansal 8 years agoPosted 8 years ago. Direct link to Nayan Bansal's post “What are these new ratios...” What are these new ratios used for? • (71 votes) Anthony Natoli 8 years agoPosted 8 years ago. Direct link to Anthony Natoli's post “Eventually, in calculus, ...” Eventually, in calculus, you will need sec(x), csc(x), and cot(x) for the derivative (rate of change) of some of the trigonometric functions. In particular, the first derivative of tan(x) is (sec(x) )^2 (119 votes) Shambhavi 8 years agoPosted 8 years ago. Direct link to Shambhavi's post “What is cosh, sinh, and t...” What is cosh, sinh, and tanh? I saw these functions on the calculator. • (29 votes) T H 8 years agoPosted 8 years ago. Direct link to T H's post “Those are hyperbolic func...” Those are hyperbolic functions: Joaquin Butial 8 years agoPosted 8 years ago. Direct link to Joaquin Butial's post “Why do you need these fun...” Why do you need these functions if you already have sine, cosine, and tangent? • (13 votes) Matthew Daly 8 years agoPosted 8 years ago. Direct link to Matthew Daly's post “Strictly speaking, we don...” Strictly speaking, we don't these days. Historically speaking, finding trig values and reciprocals were much much harder than pressing two buttons on a scientific calculator. So people wanted to have separate tables for looking up 1/sin x and so on. In fact, those weren't the only "extra" trig tables people had back then. Check out this fun article! (72 votes) Wellmaster 10 months agoPosted 10 months ago. Direct link to Wellmaster's post “Wouldn't it make more sen...” Wouldn't it make more sense for "secant" to be sin, and "cosecant" cos? There is no good reason for it to be the other way around than to absolutely troll us • (35 votes) yasmin 5 months agoPosted 5 months ago. Direct link to yasmin's post “secant and cosecant are c...” secant and cosecant are cofunctions! (3 votes) rebecca hu 8 years agoPosted 8 years ago. Direct link to rebecca hu's post “How would you find the si...” How would you find the sin, cosine, or tangent of 90 degrees? doctorfoxphd 8 years agoPosted 8 years ago. Direct link to doctorfoxphd's post “Well, sin of 90 degrees m...” Well, sin of 90 degrees means that you are trying to find the opposite over hypotenuse of a triangle with a measure of 90 degrees. But the opposite side to a 90 degree angle IS the hypotenuse. We usually tackle these angles when we have moved to the unit circle because they don't fit the Soh Cah Toa rule. Sin of 90 degrees is one. Cos of 90 degrees is 0, because if the angle has rotated through 90 degrees, there is nothing left of the adjacent side. Tangent is the sine divided by the cosine, so if Sine of 90 degrees is one and Cosine of 90 degrees is zero, you have 1/0 which is In fact, you get an error message if you ask a calculator to give you tangent of 90. (26 votes) Alexis 8 years agoPosted 8 years ago. Direct link to Alexis's post “I created Cho Sha Cao. Ho...” I created Cho Sha Cao. However I don't recommend using it because you can easily mix Cho and Cao up. • (18 votes) creationtribe 5 years agoPosted 5 years ago. Direct link to creationtribe's post “I don't like using Soh Ca...” I don't like using Soh Cah Toa. First, the 'h' is silent in two of them, so that's a first layer of decoding it in your head. Then, they're single letters that you have to plug into their original term, which is another layer of decoding, and then you have to go through and put it all together. To me it's a messy mnemonic. It's easy to start the rhythm with: I dunno - it works a billion times better for me than Soh Cah Toa shrugs • (10 votes) Polina Vitić 5 years agoPosted 5 years ago. Direct link to Polina Vitić's post “I think your alternate mn...” I think your alternate mnemonic works great! The whole point is to help you remember facts (in this case, the relationships between the trig functions and the sides of a right triangle). The best mnemonics are the ones you make up that are meaningful to you, because they will be easier to remember and work better. (12 votes) C4LOwenZ a year agoPosted a year ago. Direct link to C4LOwenZ's post “In the sections for secan...” In the sections for secant and cosecant, the article said that secant is the reciprocal of cosine and that cosecant is the reciprocal of sine. Isn't it supposed to be the other way around? • (4 votes) CrazNoah 10 months agoPosted 10 months ago. Direct link to CrazNoah's post “An easy way to remember i...” An easy way to remember is that each group only has one "co" (8 votes) Mahati 8 years agoPosted 8 years ago. Direct link to Mahati's post “So what is the exact diff...” So what is the exact difference between cosecant, secant, cotangent and cos-1, sin-1, tan-1? • (4 votes) Namitha Suresh 8 years agoPosted 8 years ago. Direct link to Namitha Suresh's post “cosecant, secant and tang...” cosecant, secant and tangent are the reciprocals of sine, cosine and tangent. (6 votes) Adhya Anil Kumar 7 years agoPosted 7 years ago. Direct link to Adhya Anil Kumar's post “Are there any other ratio...” Are there any other ratios we will learn in the future? • (2 votes) harsh ♡ 7 years agoPosted 7 years ago. Direct link to harsh ♡'s post “Well, the textbook answer...” Well, the textbook answer is that there are only 6 trig ratios, which we have already covered. However, if you really want to devel into the topic, the historical answer would be that there are at least 12 ratios, which include the ones we've learned and some new ones which are versine, haversine, coversine, hacoversine, exsecant, and excosecant. They can be expressed as the following: (7 votes)Want to join the conversation?
sinh x = ½(e^x - e^(-x))
cosh x = ½(e^x + e^(-x))
tanh x = sinh x / cosh x = (e^x - e^(-x)) / (e^x + e^(-x))
http://blogs.scientificamerican.com/roots-of-unity/10-secret-trig-functions-your-math-teachers-never-taught-you/
So, why do we still hold on to secant, cosecant, and cotangent when we dropped stuff like havercosine and excosecant? A good reason is that they make the trig formulas in calculus a little easier to remember and use, and also because the geometric meaning of the secant can be valuable at times. But other than that, they totally take a back seat to the three principal trig functions.
like how sin(x) = cos(90-x), sec(x) = csc(90-x)
cosine and sin are cofunctions of eachother, as how cosecant and secant are cofunctions of eachother!
hope this helped :)undefined
I prefer:
"Opp Hy" (sounds like 'up high')
"Add Hy" ('add height')
"Opp Add" (like an 'op ed' article)
"Sine Opp Hy" (sounds like 'Sign up high') easy
then you just know that cosine comes after sine, and tangent is last because we all know that Op Ed articles can go off on tangents.
sin-1, cos-1 & tan-1 are the inverse, NOT the reciprocal. That means sin-1 or inverse sine is the angle θ for which sinθ is a particular value. For example, sin30 = 1/2. sin-1 (1/2) = 30.
For more explanation, check this out.
https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/trig-solve-for-an-angle/a/inverse-trig-functions-intro
versine(θ) = 2 sin2(θ/2) = 1 – cos(θ)
haversine(θ)= sin2(θ/2)
coversine(θ)= 1 – sin(θ)
hacoversine(θ)= 1/2(1-sin(θ))
exsecant(θ)= sec(θ) – 1
excosecant(θ)= csc(θ) – 1
