Question

PLEASE HELP I WILL MEDAL AND FAN!

Use the given function values and trigonometric values (including the cofunction identities), to find the indicated trigonometric function.

Sintheta = 3/√13
Costheta = 3/√13
Find tan(90-theta).

PLEASe help I WILL MEDAL.

Answer 1

`tan(90-{\theta})=1`.

Explanation:

In order to find the indicated trigonometric function that is:
`tan(90-{\theta})`, we take
`sin{\theta}=(3)/(√(13))` and
`cos{\theta}=(3)/(√(13))`.

Now,
`\frac{sin{\theta}}{cos{\theta}}=((3)/(√(13)))/((3)/(√(13)))`

⇒
`tan{\theta}=1`

⇒
`{\theta}=tan^(-1)(1)`

⇒
`{\theta}=45^{{\circ}}`

Now, the value of the trigonometric function is given by:

`tan(90-{\theta})=tan(90-45)=cot45=1`

Thus,
`tan(90-{\theta})=1`.