Question

Find the value of the following angles:
(i) sin (150) (ii) cos (210)
(iii) sin(-45) (iv) tan (-30)​

Answer 1

Answer:

sin 150 is 1/2

Step-by-step explanation:

because sin is positive in 2 nd quadrant and it changes to cos 60 hence it is 1/2

cos 210 is

Answer 2

${\boxed{\mathtt{\green{Solution}}}}$

Sin ( 150° )

➾ We know that 150° = 180° - 30°

➾ So replacing 150° by ( 180° - 30°)

➾ Sin (180° - 30°)

➾ Now we know that Sin 150° is in II quadrant. And in 2nd quadrant Sine theta is Positive .

➾ Sin (180-30) = Sin 30°

${ \boxed{ \mathtt\red{ \sin(150) = \frac{1}{2} }}}$

Cos (210°)

210° = 180° + 30°

➾ Replacing 210° by 180 + 30°

➾ Cos ( 180° + 30° )

Now we know that cos 210° lies in III quadrant . And Cos function is negative there .

➾ Cos (180 + 30) = - Cos 30°

${ \boxed{ \mathtt{ \red{ \cos(210) = \: - \frac{ \sqrt{3} }{2} }}}}$

Sin ( - 45°)

➾ Sin (-45°) = -Sin 45°

We know that sin 45° = 1/√2 , So

${ \boxed{ \mathtt{ \red{ \sin( - 45) = - \frac{1}{ \sqrt{2} } }}}}$

Tan ( - 30°)

➾ tan (-30) = - tan (30°)

We know that tan 30° = 1/√3 , So

${ \boxed{ \mathtt{ \red{ \tan( - 30) = - \frac{1}{ \sqrt{3} } }}}}$

________________________

To remember that which function is negative in which quadrant I have a trick for you .

Add Sugar To Coffee.

1st word (A ) → All trigonometric functions are positive in 1st quadrant

2nd word (S) → Sine and Cosine are positive in 2nd quadrant.

3rd word( T) → Tan and cot are positive in 3rd quadrant.

4th word ( C) → Cos and sec are positive in 4th quadrant.