Question

plz try to answer with process
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Answer 1

★ Solution ❶ :-

Given

cosθ = 9/15

We need to find

tanθ , secθ & sinθ

If cosθ = 9/15

That means

• Adjacent side of θ = 9
• Hypotenuse of ∆ = 15

Now , finding opposite side of θ by Pythagoras theorem

(Hypotenuse)² = (base)² + (height)²

Here , base is the adjacent side of θ

15² = 9² + H²

225 - 81 = H²

H² = 144

H = √144

H = 12

Now ,

♦ tanθ = opposite/adjacent = 12/9

♦ secθ = hypotenuse/adjacent = 15/9

♦ sinθ = opposite/hypotenuse = 12/15

★ Solution ❷ :-

Given,

3secθ = 5

secθ = 5/3

We need to find

cosθ & tanθ

If secθ = 5/3

That means

• Hypotenuse side of ∆ = 5
• adjacent side of θ = 3

Now, finding opposite side of θ using Pythagoras theorem

(Hyp)² = (base)² + (height)²

5² = 3² + h²

h² = 25 - 15

h = √10

Now,

♦ cosθ = adj/hyp = 3/5

♦ tanθ = opp/adj = √10/3

★ Solution ❸ :-

Given,

cosecθ = 17/8

We need to find

sinθ , cosθ

If cosecθ = 17/8 , sinθ = 8/17

Because cosecθ & sinθ both are reciprocal to each other.

Now , finding cosθ using the first trigonometric identity

sin²θ + cos²θ = 1

Simplifying

cosθ = ±√1 - sin²θ

Now , substituting the value of sinθ

cosθ = √1 - (8/17)²

cosθ = √1 - 64/289

cosθ = √289 - 64/289

cosθ = √225/√289

cosθ = 15/17

Answers

♦ sinθ = 8/17

♦ cosθ = 15/17