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Trignometery: prove that .....

Square root of 1 - cos x / 1 + cos x = cosec x - cot x = 1 + sin x - cos x / 1 + sin x + cos x

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Posted on Oct 22, 2008

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How do I use secant, cosecant, and cotangent?


Use the formulas
sec(x)=1/cos(x)
csc(x)=1/sin(x)
cot(x)=1/tan(x)

Jul 04, 2015 | Casio FX570MS Scientific Calculator

1 Answer

How do you calculate sec174?


SEC, CSC & COT are the INVERSE of COS, SIN & TAN and are usually require hitting the "2nd F" or "Func" key of the calc to make:


SIN button work as COSEC,

COS button work as SEC

TAN button work as COT


Formulas are below:


sec x = 1
cos x

cosec x = 1
sin x

cot x = 1 = cos x
tan x sin x

Good luck!

Feb 05, 2013 | Sharp EL531 Scientific Calculator

1 Answer

I have a TI-84 Plus Silver Edition calculator and I need to find the inverse key to get values for sin, cos, tan, csc, sec, cot. I'm past the lesson where you use the 2nd/sin, cos tan to find the...


There are no keys for cosecant, secant, and cotangent. You can calculate those ratios as

csc(x) = 1/sin(x)

sec(x) = 1/cos(x)

cot(x) = 1/tan(x)

Simply calculate the trig ratio on the right and then take its reciprocal.

Dec 14, 2010 | Texas Instruments TI-83 Plus Calculator

2 Answers

How do I put cosecant, secant, and cotangent functions into my ti-84 plus?


By definition
  1. cosecant of X =1/sin(X), must not be confused with arc sine [sin^-1]
  2. secant of X =1/cos(X), must not be confused with arc cosine [cos^-1]
  3. cotangent of X =1/tan(X), must not be confused with arc tangent [tan^-1]
Because of these simple relations, calculator makers do not implement them with specific key sequences.
On this calculator, you have two ways to calculate one of these functions. EX cosecant of 37 degrees
  1. You enter 1 / [sin] 37 [ ) ] [ENTER] result is 1.661640141
  2. You enter [sin] [ ) ] 37 [ENTER] followed by [X^-1] to take the reciprocal of the previous answer. The [X^-1] key is the one just below [MATH].
A word of caution: secant cosecant and cotangent must not be confused with the inverse trigonometric functions arcsin, arccos, arctan

Jan 21, 2010 | Texas Instruments TI-84 Plus Calculator

1 Answer

Need to know how to obtain the cot,csc, and see in the degree mode and radian mode


Hello,
There are no dedicated keys for these trigonometric functions, for the simple reason that they can be obtained from the tan, sin, and cos by a simple division.
cotangent (x) =1/tan(x) . Do not confuse with the arc tangent tan^(-1)
cosecant (x) = 1/sin(x) . Do not confuse with the arcsine sin^(-1)
secant(x) =1/cos(x) Do not confuse with the arccosine cos^(-10)

If you know how to use the tan, cos, and sin, with angle unit in degrees or radians, then there will not be any problem

If angle unit is degree, any number you give a trigonometric function is interpreted as degree. For instance if mode is in degree , and you calculate cos(PI) do not expect the value -1. You will have the value corresponding to the cosine of of 3.14159 degrees, namely 0.99849715

Now for you if you are interested.
If [MODE] is in degrees you can still enter angles in radians
You use the [2nd][ANGLE] [3: raised r] [ENTeR].
Here is a screen capture to show you more clearly.

fc7187b.jpg
The raised r is obtained by [2nd][ANGLE][3: raised r] [ENTER]

Hope it helps.

Oct 13, 2009 | Texas Instruments TI-83 Plus Calculator

1 Answer

(1+cotx-cosecx)(1+tanx+secx)=2


I shall attempt :D
1) cosec A + cot A = 3
we know that (cot A)^2 + 1 = (cosec A)^2
Hence, (cosec A)^2 - (cot A)^2 = 1
thus, (cosec A + cot A) (cosec A - cot A) = 1
3 (cosec A - cot A) = 1
(cosec A - cot A) = 1/3

(cosec A - cot A) = 1/3
(cosec A + cot A) = 3
Summing them, 2 cosec A = 3 1/3
cosec A = 6 2/3 = 5/3
sin A = 0.15
Thus, cos A = sqrt (1 - (sin A)^2) = 0.989


2) Prove that (1+tan x - sec x)(1 + cot x + cosec x) =2
expand
LHS= 1 + cot x + cosec x + tan x + 1 + tan x cosec x - sec x - sec x cot x - sec x cosec x
We can calculate that
tan x cosec x = sec x (since tan x = sin x / cos x)
sec x cot x = cosec x
so the above is
LHS = 1 + cot x + cosec x + tan x + 1 + sec x - sec x - cosec x - sec x cosec x
LHS = 2 + cot x + tan x - sec x cosec x
LHS = 2 + cos x / sin x + sin x / cos x - 1 / (sin x cos x)
LHS = 2 + [{cos x}^2 + {sin x}^2 - 1] / (sin x cos x)
LHS = 2 (proved)

May 12, 2009 | ValuSoft Bible Collection (10281) for PC

1 Answer

Help


sec^4X- sec^2X = 1/cot^4X + 1/cot^2X
RHS
1/cot^4X + 1/cot^2X
=1/(Cos^4X/Sin^4X) + 1/(Cos^2X/Sin^2X)
=Sin^4X/Cos^4X + Sin^2X/Cos^2X
=Sin^4X/Cos^4X + Cos^2X.Sin^2X/Cos^4X
=Sin^2X/Cos^4(Sin^2X + Cos^2X)
=Sin^2X/Cos^4X
=(1-Cos^2X)/Cos^4X
=1/Cos^4X - Cos^2X/Cos^4X
=1/Cos^4X - 1/Cos^2X
=Sec^4X - Sec^2X
=LHS

Feb 02, 2009 | Super Tutor Trigonometry (ESDTRIG) for PC

1 Answer

Solve it plz......


cos x + root 3 sin x =root 2
cos x + ö3 * Sin x = ö2
squaring both the side
(cos x + ö3 * Sin x)2 = (ö2)2
Cos2 x + 3 * Sin2 x = 2
Cos2 x + Sin2 x + 2 * Sin2 x = 2
1 + 2 * Sin2 x= 2
2 * Sin2 x = 2-1
2 * Sin2 x = 1
Sin2 x = ½
Sin x = ö½
Sin x = 1/V2= Sin 45
X = 450

Aug 28, 2008 | Super Tutor Trigonometry (ESDTRIG) for PC

1 Answer

Trigonometry proofs


tan y/sin y = sec y; Can you sho me how to prove this?

Aug 05, 2008 | Super Tutor Trigonometry (ESDTRIG) for PC

4 Answers

Trig Identities


Change csc to 1/sin. Find a common denominator and add the two left terms.
1/sin - sin = (1 -sin^2)/sin. Rewrite formula
(1 - sin^2)/sin = cos^2/sin Divide out the /sin.
1 - sin^2 = cos^2 Rearange.
1 = cos^2 + sin^2 Yes, that's true. It's like the Pythagorean formula.

May 22, 2008 | Super Tutor Trigonometry (ESDTRIG) for PC

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