Question

if cos theta is equal to 24 upon 25 find sin theta and tan theta​

Answer 1

Answer:

$\frac{7}{25}$

$\frac{7}{24}$

Step-by-step explanation:

 CosΦ=$\frac{24}{25}$

We know cosΦ=$\frac{base}{hypotenus}$

Applying pythagorean theorem.

H² = B² + P²

We know H and B

P = √625-576

   =7

Now

Tan∅=$\frac{P}{B}$

      =$\frac{7}{24}$

Sin∅=$\frac{7}{25}$

Answer 2

$sin\ \theta = \frac{7}{25} \text{ and } tan\ \theta = \frac{7}{24}$

Solution:

Given that,

$cos\ \theta = \frac{24}{25}$

By definition of cos,

$cos\ \theta = \frac{adjacent}{hypotenuse}$

Therefore,

adjacent = 24

hypotenuse = 25

By pythagoras theorem,

$hypotenuse^2 = opposite^2 + adjacent^2\\\\Therefore,\\\\25^2 = opposite^2 + 24^2\\\\625 = opposite^2 + 576\\\\opposite^2 = 625 - 576\\\\opposite^2 = 49\\\\Therefore,\\\\opposite = 7$

Find sin theta:

$sin\ \theta = \frac{opposite}{hypotenuse}\\\\sin\ \theta = \frac{7}{25}$

Find tan theta:

$tan\ \theta = \frac{opposite}{adjacent}\\\\tan\ \theta = \frac{7}{24}$

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