Question

if tan B=√3 find sin B and cos B​

Answer 1

❥A᭄ɴsᴡᴇʀ࿐

we know that

tanθ=

sideadjacenttoangleθ

sideoppositetoangleθ

ortanθ=

Base

Perpendicular

Given: tanB=

3

tanB=

1

3

tanB=

1

3

⇒

B

P

=

1

3

⇒

AB

AC

=

1

3

Let

side opposite to angle B=AC=

3

k

side adjacent to angle B=aB=1k

where k is any positive integer

Firstly we have to find the value of BC

so we can find the value of AC with help of Pythagoras theorem.

⇒(AB)

2

+(AC)

2

=(BC)

2

⇒(1k)

2

+(

3

k)

2

=(BC)

2

⇒(BC)

2

=1k

2

+3k

2

⇒(BC)

2

=4k

2

⇒BC=

4k

2

=±2k

but side can't be negative so, BC=2k

Now we will find sinB and cosB

we know that

sinθ=

hypotenuse

sideoppositetoangleθ

side opposite to angle B=AC=k

3

Hypotenuse =BC=2k

so, sinB=

BC

AC

=

2k

3

k

=

2

3

Now we know that

cosθ=

hypotenuse

sideadjacenttoangleθ

side adjacent to angle B=AB=1k

Hypotenuse =BC=2k

So, cosB=

BC

AB

=

2k

1k

=

2

Answer 2

Answer:

sinb=

$\sqrt(3) \div 2$

cos b

$1 \div 2$