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DedPeter [7]
3 years ago
5

Last one! 50 points!​

Mathematics
2 answers:
Zinaida [17]3 years ago
7 0
<h3>SOLUTION :</h3>

<u>Given that</u> :

\frak {\cos( \theta_{1} )  =   -  \frac{13}{15} }

<u>To find</u> :

\frak{  sin( \theta_{1}  )}

We know that cos θ is base/hypotentuse

So, here the base is -13 and the hypotentuse is 15

As we got the base and hypotentuse, perpendicular needs to be found out

Now, applying <u>Pythagoras </u><u>Theorem</u>

According to Pythagoras theorem we know that :

  • (Hypotentuse)² = (Base)² + (Perpendicular)²

Let us assume perpendicular be x

Putting the values we get

  • (15)² = (-13)² + (x)²

  • 225 = 169 + x²

By transposing we get

  • x² = 225 - 169

  • x = √56

  • x = 2√14

<u>sin θ formula : Perpendicular/Hypotentuse</u>

\star \:  \:  \underline{ \overline{ \boxed{ \frak{ sin (\theta_{1})} =  \frac{-2 \sqrt{14} }{15} }}}

<u>Hence, the answer is </u><u>-</u><u>2√14/15</u>

Ipatiy [6.2K]3 years ago
4 0

Answer:

sin theta = -2 sqrt(14)/15

Step-by-step explanation:

cos theta = adj / hyp

We can find the opp side by using the Pythagorean theorem

adj ^2 + opp ^2 = hyp^2

(-13)^2 + opp ^2 = 15^2

169 + opp ^2 = 225

opp ^2 = 225 -169

opp ^2 =56

Taking the square root of each side

sqrt( opp^2) = sqrt(56)

opp = sqrt(4 * 14)

opp = 2 sqrt(14)

Since we are in the third quadrant opp is negative

opp = -2 sqrt(14)

We know

sin theta = opp / hyp

sin theta = -2 sqrt(14)/15

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