SOLUTION: Use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function 0° ≤ 𝛼 ≤ 90°, 0 ≤ 𝛼 ≤ 𝜋 2

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Question 1203872: Use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function
0° ≤ 𝛼 ≤ 90°, 0 ≤ 𝛼 ≤
𝜋
2
.
cot(𝛼) = 3
(a)
tan(𝛼)

(b)
csc(𝛼)

(c)
sec(𝛼)

(d)
sin(𝛼)

Found 2 solutions by Theo, MathLover1:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
you are given that cot(theta) = 3
cot(theta) = adjacent side divided by opposite side.

if adjacent side is 3, then opposite side is 1.
use pythagorus to solve for hypotenuse.
pythagorus says that hypotenuse squared = adjacent side squared plus opposite side square.
you get hypotenuse squared = 3^2 + 1^2 = 9 + 1 = 10
this makes hypotenuse = sqrt(10)
you have:
adjacent side = 3
opposite side = 1
hypotenuse = 10

(a)
tan(𝛼) = opposite side / adjacent side = 1/3

(b)
csc(𝛼) = hypotenuse / opposite side = sqrt(10)/1 = sqrt(10)

(c)
sec(𝛼) = hypotenuse / adjacent side = sqrt(10)/3

(d)
sin(𝛼) = opposite side / hypotenuse = 1/sqrt(10)

here's a diagram with all the basic trig functions identified.

Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!

Use the definition of cotangent to find the known sides of the unit circle

so,

which is same as

so, and

then hypothenuse is:

(a)

(b)

(c)

(d)