Question

Help please explanation as detailed as you can make it but easy to understand

Answer 1

tan(x) = (√6)/2

Explanation:

The tangent identity is ...

tan = sin/cos

Substitution

Substituting the given values of sine and cosine, we have ...

`tan(x)=(sin(x))/(cos(x))=((42)/(55))/((14√(6))/(55))`

Simplification

At this point, it becomes a problem in simplifying a compound fraction. This can be done by dividing the fractions in the usual way, and cancelling common factors from numerator and denominator.

We note the denominators (55) are the same, and that 42=3·14, so we can simplify this to ...

`tan(x)=(3)/(√(6))=(3\cdot√(6))/(√(6)\cdot√(6))=(3√(6))/(6)\\\\\boxed{tan(x)=(√(6))/(2)}`

The step of multiplying by (√6)/(√6) is for the purpose of "rationalizing the denominator," making the denominator a rational number: (√6)² = 6.

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Additional comment

If sin(x) = 42/55, then cos(x) = (√1261)/55. There is no angle x that will have these values of its trig functions. (Another example of poor curriculum editing.)