1 Answer

Digger · Answer 1 · 2023-08-15T17:04:17+0000

Given:

$tan\theta=(1)/(7)\text{ and sin}\theta<0$

Required:

Find the value of cos in Radical form.

Step-by-step explanation:

Use the trigonometric ratio:

$\begin{gathered} tan\theta=(opp.)/(adj.) \\ tan\theta=(1)/(7) \end{gathered}$

Therefore opp. = 1 and adj. = 7

Find the hypotenuse by using the Pythagoras theorem.

$\begin{gathered} hyp.=√((opp.)^2+(adj.)^2) \\ hyp.=√((1)^2+(7)^2) \\ hyp.=√(1+49) \\ hyp.=√(50) \end{gathered}$

Use the trigonometric ratio for cosine as:

$\begin{gathered} cos\theta=(adj.)/(hyp.) \\ cos\theta=(7)/(√(50)) \end{gathered}$

Given that sin < 0 and tan = 1/7 > 0

It will be possible only when cos < 0

So

$cos\theta=-(7)/(√(50))$

Final Answer:

$cos\theta=-(7)/(√(50))$

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