Q7 of 268 Page 4

If then find the values of cos θ and tan θ.

Given:

We know that,

Let,

Perpendicular =AB =4k

and Hypotenuse =AC =5k

where, k is any positive integer

So, by Pythagoras theorem, we can find the third side of a triangle

In right angled ∆ ABC, we have

⇒ (AB)² + (BC)² = (AC)²

⇒ (4k)² + (BC)² = (5k)²

⇒ 16k² + (BC)² = 25k²

⇒ (BC)² = 25 k² –16 k²

⇒ (BC)² = 9 k²

⇒ BC =√9 k²

⇒ BC =±3k

But side BC can’t be negative. So, BC = 3k

Now, we have to find the value of cos θ and tan θ

We know that,

The side adjacent to angle θ or base = BC =3k

Hypotenuse = AC =5k

So,

Now,

We know that,

Perpendicular = AB =4k

Base = BC =3k

So,

Find the value of the following : (a) sin θ (b) cos θ (c) tan θ from the figures given below :

In ∆PQR, ∠Q is a right angle PQ = 3, QR = 4. If ∠P=α and ∠R=β, then find the values of

(i) sin α (ii) cos α

(iii) tan α (iv) sin β

(v) cos β (vi) tan β

If calculate cos A and tan A.

If then find the values cos θ and tan θ.