Question

if tan theta is 5/12,find sin theta and cos theta​

Answer 1

Answer:

here sin theta = 5/13 , and cos theta = 12/13

Step-by-step explanation:

so here tan theta = 5/12 [ as given ]

tan=opposite/adjecent  so sin=opposite/hypo and cos = adjecent/hypo

so here 5 is opposite and and 12 is adjecent so hypo=x

so sin = 5/x and cos=12/x

now lets find x by pythogerous therom

x2= [5]2 + [12]2 [ here there is 5 square and 12 square ]

x2= 25+144= 169

so root 169=13

so sin = 5/13 and cos = 12/13

Answer 2

Solution

Given :-

• tan θ = 5/12

Find :-

• sin θ & cos θ

Explanation

Using Formula

★ tan θ = perpendicular/Base

★cos θ = Base/Hypotenuse

Then, Assume that,

ABC be a triangle.

Where,

• AB = Perpendicular = 5
• BC = Base = 12
• CA = Hypotenuse

Now, first Calculate Hypotenuse(CA)

Using Pythagoras's Theorem.

★ (Hypotenuse)² = (Perpendicular)² +(Base)²

Keep all above values

➡ CA² = 5² + 12²

➡ CA² = 25 + 144

➡ CA² = 169

➡ CA = √(169)

➡ CA = 13

Since

• Hypotenuse will be CA = 13

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Now, Calculate sin θ,

★ sin θ = perpendicular/Hypotenuse

➡ sin θ = 5/13

Now, Calculate cos θ

➡ cos θ = Base/Hypotenuse

➡cos θ = 12/13

Hence

• Value of sin θ = 5/13
• Value of cos θ = 12/13

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