Find the six trigonometric functions given a point calculator

Trigonometry Function Calculator

Use the Trigonometry Calculator to calculate the value of any trigonometry function.

Please select between radians and degrees first!

Usual values used in trigonometry

Π(pi) = 3.1415 ;          Π/2(pi/2) = 1.5707 ;
Π/3(pi/3) = 1.0471 ;    Π/4(pi/4) = 0.7853 ;
Π/5(pi/5) = 0.6283 ;    Π/6(pi/6) = 0.5235 ;
Π/7(pi/7) = 0.4488 ;    Π/8(pi/8) = 0.3927 ;
Π/9(pi/9) = 0.3490 ;    Π/10(pi/10) = 0.3141 ;

2Π (2*pi) = 6.2831 ;    3Π (3*pi) = 9.4247 ;
4Π (4*pi) = 12.5663 ;    5Π (5*pi) = 15.7079 ;
6Π (6*pi) = 18.8595 ;    7Π (7*pi) = 21.9911 ;
8Π (8*pi) = 25.1387 ;    9Π (9*pi) = 28.2743 ;
10Π (10*pi) = 31.4159 ;

Explanation:

If the point is given on the terminal side of an angle, then:

Calculate the distance between the point given and the origin:

#r=sqrt(x^2+y^2)#

Here it is: #r=sqrt(7^2+24^2)=sqrt(49+576)=sqrt(625)=25#

Now we can calculate all 6 trig, functions:

#sinalpha=y/r=24/25#

#cosalpha=x/r=7/25#

#tanalpha=y/x=24/7=1 3/7#

#cotalpha=x/y=7/24#

#secalpha=r/x=25/7=3 4/7#

#csc alpha=r/y=25/24= 1 1/24#

Method and examples

Trigonometry

Method

1. Simplifying trigonometric equations, proving identities Expression     `sin^2(30)*cos^2(60)` `sin(30)*cos(60)+sin(30)*cos(60)` `sin(30)*csc(30)-sin(60)*csc(60)` `2sin^2(30)*3cos^2(60)` `(2tan(60))/(1+tan^2(60))` `(3sec(60)+2tan(45)+csc(30))/(sin^2(60)+cot^2(45))` `(3sec(60)+2tan(45)+csc(30))(sin^2(60)+cot^2(45))` `sin(30)*cos(45)*tan(60)=sin(45)*cos(60)*cot(30)` `tan(45)*sec(72)*sin(58)=cos(32)*csc(18)` `sin^2(34)-cot^2(46)-cos^2(56)+tan^2(44)=sec^2(62)-csc^2(28)` `sin(30)*cos(45)*tan(60)=sin(45)*cos(60)*cot(30)` `tan(45)*sec(72)*sin(58)=cos(32)*csc(18)` `sin^2(34)-cot^2(46)-cos^2(56)+tan^2(44)=sec^2(62)-csc^2(28)` `sin^2(50)+sin^2(40)=1` `sin(35)*sec(55)-cos(55)*csc(35)=tan(25)-cot(65)` `2sin(30)+2tan(45)-3cos(60)-2cos^2(30)=0` `2sec^2(x)-2` `sin(x)sec(x)` `sin(x)cot(x)` `cot(x)sin(x)` `tan(x)+cot(x)` `cos(x)+cot(x)` `tan(x)sin(x)+cos(x)` `cot^4(x)+cot^2(x)` `cos^2(x)csc^2(x)-cos^2(x)` `tan^2(x)-sin^2(x)` `(csc(x)-sin(x))(sec(x)-cos(x))` `(tan(x)+cot(x))(sec(x)-cos(x))(csc(x)-sin(x))` `1+1/tan^2(x)` `csc(x)/cos(x)-cos(x)/sin(x)` `sec(x)/2(tan(x)+cot(x))` `sec(x)/(2(tan(x)+cot(x)))` `(tan^2(x)-cot^2(x))/(sin^2(x)-cos^2(x))` `(tan^2(x)+cot^2(x))/(tan^2(x)-cot^2(x))` `(tan^2(x)-cot^2(x))/(tan^2(x)+cot^2(x))` `(3sin(x)+5cos(x))^2+(3cos(x)-5sin(x))^2` `(1+cos(x))/sin(x)+sin(x)/(1+cos(x))` `sin^2(x)cos(x)+sin^3(x)+cos^2(x)sin(x)+cos^3(x)` `(sin^4(x)-cos^4(x))/(sin^2(x)-cos^2(x))` `5cos^2(x)+2sin^2(x)` `2cos^2(x)+sin^2(x)` `(sin^4(x)+cos^4(x))` 2. Find the value of all the other five trigonometric functions or solve expression If = in then   1. Find the value of all the other five trigonometric functions sin(x) cos(x) tan(x) csc(x) sec(x) cot(x)   2. Solve expression If `sin(x)=5/13` then find other trigonometry If `cos(x)=12/13` then find other trigonometry If `tan(x)=5/12` then find other trigonometry If `csc(x)=13/5` then find other trigonometry If `sec(x)=13/12` then find other trigonometry If `cot(x)=12/5` then find other trigonometry If `sin(x)=3/5` then solve `cos(x)csc(x)+tan(x)sec(x)` If `tan(x)=1/2` then solve `(1-tan^2(x))/(1+tan^2(x))+(2tan(x))/(1+tan^2(x))` If `sin(x)=4/5` then solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))` If `cos(x)=3/5` then solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))` 3. For P(3,4), find the value of all six trigonometric functions P ( , )     `(3,4)` `(15,8)` `(-8,6)` `(7,-24)`

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