Question

if sin theta = 3/5 and cos theta = 4/5, then find tan theta and cot theta​

Answer 1

Answer:

tan@=sin@÷cos@

tan@=(3÷5)÷(4÷5)

tan@=3/4

cot@=4/3

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Answer 2

Given:

• sinФ = 3/5
• cosФ = 4/5

To find:

The value of

1. tanФ
2. cotФ

So,

We know that,

sinФ = P/H

cosФ = B/H

tanФ =  P/B

cotФ = B/P

Now,

sinФ = P/H = 3/5

So, let P = 3k and H = 5k

We can get B,

⇒ B² = H² - P²

⇒ B² = (5k)² - (3k)²

⇒ B² = 25k² - 9k²

⇒ B² = 16k²

⇒ B = 4k

And,

Also cosФ = B/H = 4/5

B = 4k and H = 5k

So,

P = 3k , B = 4k , H = 5k

Now,

• Finding

tanФ = P/B = 3k/4k = 3/4

And

cotФ = B/P = 4k/3k = 4/3

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More information:

• P = Perpendicular
• B = Base
• H = Hypotenuse

Also,

• sinФ = 1/(cosecФ)
• cosecФ = 1/(sinФ)
• cosФ = 1/(secФ)
• secФ = 1/(cosФ)
• tanФ = 1(cotФ)
• cotФ = 1/(tanФ)

• sin(90° - Ф) = cosФ
• cos(90° - Ф) = sinФ
• tan(90° - Ф) = cotФ
• cot(90° - Ф) = tanФ
• sec(90° - Ф) = cosecФ
• cosec(90° - Ф) = secФ