If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Trigonometry

Course: Trigonometry>Unit 1

Lesson 7: The reciprocal trigonometric ratios

Finding reciprocal trig ratios

Sal finds all six trigonometric ratios (sine, cosine, tangent, secant, cosecant, and cotangent) of an angle in a given right triangle. Created by Sal Khan.

Want to join the conversation?

• What is the full form of csc, sec and cot?
• Sin: sine
Cos: cosine
Tan: tangent
Sec: secant
Csc: cosecant
Cot: cotangent
• Okay,so now we know how to calculate sin cosin and tangent.But where do we use them!!and how are these formulae derived?
• 1 .Trig is used in many things in real life. Engineers, architects, astronomers, geologists, navigators, and scientists use them every day. for more, go here:
http://en.wikipedia.org/wiki/Trigonometry#Applications_of_trigonometry

2. Sine, cosine, and tangent are all mathematical operations. Your question is like asking where multiplication is derived. We came up with the 6 trigonometry functions trying to understand triangles.
• When would one want to use csc, sec and cot instead of sin, cos and tan?
• It's just for one's knowledge: also, when one has the angle and the opposite side and is trying to calculate the adjacent, it is easier to simplify the cotangent function than the tangent - this is also true for the other trig ratios trigx=a/b when you need to find b.

than it is to simplify

I hope that makes sense!
• is there any easy mnemonic device to remember which reciprocal functions and normal trig functions go together?
• Personally I just imagine that the reciprocal functions aren't allowed to start with the same letter as big three do:

sine and secant both start with s, so the inverse must be cosecant.
cosine and cosecant both start with c, so the inverse must be secant.

That's how my mind works, anyway. Maybe yours will agree!
• how do you do the CscA, secA amd CotA on a calculator?
• In the order that you gave me cscA = 1/sinA , secA = 1/cosA , cotA = 1/tanA. Thus take 1 over cos/sin/tan of the desired angle.
• What does reciprocal mean?
• 1. In reciprocal you have to take an integer (like 6) and then convert it into a fraction. In this case it would be 6/1.
2. Then switch the numerator and denominator. So your answer would be 1/6.

If the number is already fraction then just do step 2.

Hope this helps!

By the way: opposite reciprocal is the same thing, just change the positive sign to a negative or a negative sign to a positive.
• how can we say that sin square plus cos square equals to one
• The cosine is adjacent over hypotenuse.The sine is opposite over adjacent. So:
Cos^2(x)+sin^2(x)
hyp^2/hyp^2 (because of Pythagorean theorem)
1
A similar process can be done for sec^2(x)-tan^2(x)=1 and csc^2(x)-cot^2(x)=1
• Are the csc,sec,and cot really that helpful anyway?
• Not really. Once you leave trig class, it's mostly sin, cos and tan from then on. That's why you don't see buttons for the other ones on calculators.
• hey then sal in previous video took something as tan to power of -1 but could not he take it as cot
• Well no. Tan^-1 is the inverse of Tan which so far I have used to find the degree of an angle using the length of the sides whereas Cot is the reciprocal which I have used to find the length of lines using the degree of an angle. Hope this helps!