SOLUTION: Use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function
0° ≤ 𝜃 ≤ 90°, 0 ≤ 𝜃 ≤
𝜋
2
Algebra.Com
Question 1203868: Use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function
0° ≤ 𝜃 ≤ 90°, 0 ≤ 𝜃 ≤
𝜋
2
.
sec(𝜃) = 3
(a)
cos(𝜃)
(b)
cot(𝜃)
(c)
csc(𝜃)
(d)
sin(𝜃)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
secant(theta) = hypotenuse / adjacent side = 3
if hypotenuse = 3, then adjacent side = 1
pythagorus says that hypotenuse squared minus adjacent side squared = opposite side squared.
this means thqt 3^2 - 1^2 = opposite side squared = 8.
this means that opposite side = sqrt(8)
you have:
adjacent side = 1
opposite side = sqrt(8)
hypotenuse = 3
(a)
cos(𝜃) = adjacent side / hypotenuse = 1/3
(b)
cot(𝜃) adjacent side / opposite sidde = 1/sqrt(8)
(c)
csc(𝜃) = hypotenuse / opposite side = 3/sqrt(8)
(d)
sin(𝜃) = opposite side / hypotenuse = sqrt(8)/3
here's a diagram of the basic trig functions.
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