Question

given tan A=11/60 and that angle A is in quadrant 1, find the exact value of cos A in simplest form using a rational denominator

Answer 1

`\cos(A) = (60)/(61)`

Explanation:

Given

`\tan(A) = (11)/(60)`

`0 \le A \le 90` --- First Quadrant

Required

Find cos(A)

The tan of an angle is:

`\tan(A) = (Opposite)/(Adjacent)`

and

`\tan(A) = (11)/(60)`

By comparison:

`Opposite = 11`

`Adjacent = 60`

So, the hypotenuse is:

`Hypotenuse^2 = Adjacent^2 + Opposite^2`

`Hypotenuse^2 = 60^2 + 11^2`

`Hypotenuse^2 = 3721`

Take square roots

`Hypotenuse = \sqrt{3721`

`Hypotenuse = 61`

The cosine of an angle is:

`\cos(A) = (Adjacent)/(Hypotenuse)`

This gives:

`\cos(A) = (60)/(61)`