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If cot A=8, find the exact values of the remaining trigonometric functions for the acute angle A.​

User Joshkunz
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1 Answer

6 votes

Answer:

Cos A = 1.01

Sin A = 8.06

Cosec A = 0.1241

Sec A = 0.9926

Tan A = 1/8 = 0.1250

Explanation:

cot A = 1/tan A.

if Cot A = 8 and cot A = 1/tanA

then,

8= 1/tan A

by cross multiplying

8tan A = 1

dividing both sides by 8

tan A = 1/8

recall SOH CAH TOA

tangent = opposite/adjacent

therefore, given a right angle triangle with adjacent= 8 and opposite = 1 therefor hypotenuse will be according to pythagora's theorem,

hypotenuse^2 = opposite^2 + adjacent^2

let hypotenuse be h, opposite be o and adjacent be a

h^2 = o^2 + a^2

h^2 = 1^2 + 8^2

h^2 = 1 + 64

h^2 = 65

taking square roots of both sides we have

h = 8.06 to 2 decimal places.

sin A = opposite/ hypotenuse

Sin A = 1/8.06

Sin A = 0.1241

Cos A = adjacent/ hypotenuse

Cos A = 8/8.06

Cos A = 0.9926 to 4 significant figures

Cosec A = 1/Sin A

Cosec A = 1/0.1241

Cosec A = 8.06

Sec A = 1/Cos A

Sec A = 1/0.9926

Sec A = 1.01 to 2 decimal places.

User Polo
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