cos = 1/11, find the 5 other trig functions

Question

cos=1/11

find sin, tan, csc,sec,cot

 

please help me quickly

 

Answer 1

Jeff,

        If cos(x)=1/11 since cos = adj/hyp then hyp=11 and adj=1 and using hyp²=adj²+opp² we can solve for the opp=(hyp²+adj²)^1/2=(11²-1²)^1/2=10.954.

 

So sin(x) = 10.954/11=.9958. 

 

Can you do the rest?

 

Jim

Answer 2

Cos φ = 1/11; sec φ = 11; Sen^2φ + cos^2φ =1 => sen^2φ= 1-(1/11)^2 = (121-1)/121 = 120/121=> senφ= √(120/121) = 2√30/11;

Tan φ = sinφ/cosφ= (2√30/11)/(1/11)=2√30, You know how to calculate Cotφ = 1/tanφ and cosecφ = 1/sinφ

Answer 3

Let's assume we have a right triangle of sides a, b, c, and angles A, B, C

 

cos A = b/c = 1/11

 

So side b = 1 and c = 11.  To find a, use the Pythagorean Theorem:

 

c² = a² + b²

 

11² = a² + 1²

11² - 1² = a²

121 - 1 = a²

120 = a²

 

a = √120 = 2√30

 

We now have all three sides of the triangle: a = 2√30, b = 1, c= 11

 

cos(A) = b/c = 1/11

sin(A) = a/c =

tan(A) = a/b =

cot(A) = b/a =

sec(A) = c/b =

csc(A) = c/a =