Question

If cosθ=4/5, find all other trigonometric ratios of angle θ.

Answer 1

Answer:

Given :

cos Ф = 4 / 5

We know :

cos Ф = B / H

Also :

H² = P² + B²

P = √ ( H² - B² )

P = √ 25 - 16

P = √ 9

P = 3 .

Now we have :

H = 5 , B = 4 and P = 3 .

sin  Ф = P / H

= > 3 / 5

cos Ф = B / H

= > 4 / 5

tan Ф = P / B

= > 3 / 4

cot Ф = B / P

= > 4 / 3

sec Ф = H / B

= > 5 / 4

cosec Ф = H / P

= > 5 / 3

Therefore we get all required answer.

Answer 2

Step-by-step explanation:

Given : cosθ = 4/5

To find : All other trigonometric ratios of angle θ

★We know that cosθ = b/h

Here b = 4 and h = 5

→So, H² = P² + B²

5² = p² + 4²

25 = p² + 16

25 – 16 = p²

√9 = p²

3 = P

So now we have P= 3 , B= 4 and H= 5

• sinθ= p/h = 3/5
• cosecθ= h/p = 5/3
• cosθ = b/h = 4/5
• secθ = h/b = 5/4
• tanθ = p/b = 3/4
• cotθ= b/p = 4/3

Hope you got it ✓