How do you find the values of the other five trigonometric functions of the acute angle A with cosA=2/sqrt10?

2 Answers
EZ as pi
Oct 28, 2017

Once you have a = 2, o = sqrt6 and h = sqrt10

you can find sin, cos, tan, cot, sec and "cosec"

Explanation:

cos A = "adj"/"hyp" = 2/sqrt10

So, using Pythagoras:
"opp"^2 = sqrt10^2 -2^2 = 10-4=6

"opp" = sqrt6

You now have: a = 2, o = sqrt6 and h = sqrt10

Sin A = o/h = sqrt6/sqrt10

Cos A = a/h = 2/sqrt10

Tan A = o/a =sqrt6/2

Cot A = a/o=2/sqrt6

Sec A = h/a =sqrt10/2

"cosec" A = h/o=sqrt10/sqrt6

Jim G.
Oct 28, 2017

"see explanation"

Explanation:

"given A is acute, that is in first quadrant then all "
"trig. ratioswill be positive"

"using "sin^2A+cos^2A=1

rArrsin^2A=+-sqrt(1-sin^2A)

•color(white)(x)cosA=2/sqrt10

•color(white)(x)sinA=sqrt(1-(2/sqrt10)^2)

color(white)(xxxxxxx)=sqrt(1-4/10)=sqrt(3/5)=sqrt3/sqrt5=sqrt15/5

•color(white)(x)secA=1/cosA=sqrt10/2

•color(white)(x)cscA=1/sinA=5/sqrt15=sqrt15/3

•color(white)(x)tanA=sinA/cosA=sqrt15/5xxsqrt10/2=sqrt6/2

•color(white)(x)cotA=1/tanA=2/sqrt6=sqrt6/3

"All denominators have been rationalised"

Related questions
See all questions in Basic Trigonometric Functions
Impact of this question
3513 views around the world
You can reuse this answer
Creative Commons License