Question

If cos thita=24/25 then find: (a)sin thita (b) tan thita (c) sec thita​

Answer 1

Given

Cosθ= 24/25

To Find

a)sinθ

b) tanθ

c)secθ

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Cosθ=24/25(base/hypotenuse)

We know the hypotenuse theorem

We will apply hypotenuse theorem to find out the perpendicular.

base is 24

hypotenuse is 25

perpendicular = ?

h²= b²+p²

=>(25)²= (24)²+p²

=>625=576+p²

=>625-576= p²

=>p²=49

=>p= 7

(a) sinθ is perpendicular/hypotenuse

so,sinθ = 7/25

(b) tanθ is perpendicular/base

So,tanθ=7/24

(c)secθ is opposite of cosθ which is h/b

so,secθ=25/24

Extra information=>

Cosecθ= hypotenuse /perpendicular

Cotθ= base/perpendicular

=>cosecθ is reciprocal of sinθ

=>secθ is the reciprocal of cosθ

=>cotθ is the reciprocal of tanθ

Answer 2

Step-by-step explanation:

cos theta = 24/25

then, cos = base / hypotenuse

so, base = 24 cm

hypotenuse = 25 cm

so, bc = 25

ac= 24

so, (25)^2 = (24 x 24) + (ab x ab)

or, ab=√ (625) - (576)

or, ab = √49

or, ab= 7

then, a) sin theta = height / hypotenuse

= 7/25.

then, b) tan theta = height/base

= 7/24.

then, c) sec theta = hypotenuse/base

= 25/7.

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