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If and , find using trigonometric identities. Explain which identities to use. Please help :)

If and find using trigonometric identities Explain which identities to use Please help class=


Answer :

Answer:

tanθ = [tex]\frac{5}{12}[/tex]

Step-by-step explanation:

• tanθ = [tex]\frac{sin0}{cos0}[/tex]

given sinθ = [tex]\frac{5}{13}[/tex] , we have to find cosθ

Now sinθ = [tex]\frac{5}{13}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

This is a right triangle with opposite side 5 and hypotenuse 13

To find the adjacent side , a , use Pythagoras' identity

• a² + b² = c² ( c is the hypotenuse and a, b the legs )

let a = adjacent , b = 5 and c = 13 , then

a² + 5² = 13²

a² + 25 = 169 ( subtract 25 from both sides )

a² = 144 ( take square root of both sides )

[tex]\sqrt{a^2}[/tex] = [tex]\sqrt{144}[/tex]

a = 12

Thus the adjacent side is 12

Then cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{12}{13}[/tex]

Then

tanθ = [tex]\frac{\frac{5}{13} }{\frac{12}{13} }[/tex] = [tex]\frac{5}{13}[/tex] × [tex]\frac{13}{12}[/tex] = [tex]\frac{5}{12}[/tex]