Question

Look at the figure below: an image of a right triangle is shown with an angle labeled y If sin y° = 7 over q and tan y° = 7 over r, what is the value of sec y°?

sec y° = q over r
sec y° = 7r
sec y° = 7q
sec y° = r over q

Answer 1

`\sec y=(q)/(r)`

Explanation:

Given that,

`\sin y=(7)/(q)`

and

`\tan y=(7)/(r)`

We need to find the value of
`\sec y`. We know that,

`\sec\theta=(1)/(\cos\theta)`

Also,

`\tan\theta=(\sin\theta)/(\cos\theta)\\\\\cos\theta=(\sin\theta)/(\tan\theta)`

Substitute all the values,

`\cos y=((7)/(q))/((7)/(r))\\\\=(7)/(q)* (r)/(7)\\\\\cos y=(r)/(q)`

So,

`\sec y=(1)/((r)/(q))\\\\\sec y=(q)/(r)`

So, the correct option is (a) i.e.
`\sec y=(q)/(r)`.