Question

if sin0~=1/6, what are the values of cos0~ and tan0~? write your answer in simplified radical form PLS HELP FAST

Answer 1

cosθ =
`(√(35) )/(6)` , tanθ =
`(√(35) )/(35)`

Explanation:

given sinθ =
`(1)/(6)` =
`(opposite)/(hypotenuse)`

These ratios refer to a right triangle , with

1 being opposite to the angle θ

6 being the hypotenuse , opposite the right angle

We require to find the adjacent side (a ) , next to the angle θ

using Pythagoras' identity in the right triangle

a² + b² = c²

a and b are the sides opposite and adjacent to θ , c is the hypotenuse

a² + 1² = 6²

a² + 1 = 36 ( subtract 1 from both sides )

a² = 35 ( take square root of both sides )

`√(a^2)` =
`√(35)`

a =
`√(35)` ← adjacent side to angle θ

Then

cosθ =
`(adjacent)/(hypotenuse)` =
`(√(35) )/(6)`

tanθ =
`(opposite)/(adjacent)` =
`(1)/(√(35) )`

multiply by
`(√(35) )/(√(35) )` to rationalise the denominator

tanθ =
`(1)/(√(35) )` ×
`(√(35) )/(√(35) )` =
`(√(35) )/(35)`