Question

if sin theta = -1/2 then find the value of theta

Answer 1

If Sinθ = -1/2 then the value of θ is 210°

Given,

Sinθ = -1/2

To find,

Value of θ

Solution,

We can simply solve this problem by using the followinf proess.

Now,

According to trignometric function, the value of

Sin30°=1/2  -----> Equation 1

But we need to find the value of θ where Sinθ= -1/2

We know that the value of Sinθ is negative only in the 3rd and 4th quadrant.

According to trigonometric functions of sum and differences of two angles, Sin(180+θ)= -Sinθ

Substituting,

From equation 1,

Sin(180+30) = -Sin30°

Sin210° = -1/2

∴ θ = 210°

Hence, if Sinθ = -1/2 then the value of θ is 210°

Answer 2

The possible value of the angles in the principle branch would be 210 and 330 degrees.

Given

• sin theta = -1/2

To find

• the value of theta

solution

we are provided with the value of a trigonometric function that is sin theta and are asked to determine the value of the angle for which the trigonometric function will bear the given value of negative 1/2.

we know that trigonometry function of sin theta will take the value from negative 1 to positive one depending on the value of angle. the sign of the resultant value will be decided by the quadrant in which the angle falls.

it is simpler to find the value of the anglr for which the sin function will give positive one by two and then determine the quadrant where the function falls based on the sign of the given value that is, 1/2.

sinθ = 1/2

or, θ = 30°

now we have to determine the quadrant where the function falls.

since the given value is negative the the function should be in third quadrant or 4th quadrant.

if the function is in third quadrat,

angle, θ = 180 + 30

or, θ = 210°

if the function falls in the 4 th quadrant,

θ = 360 - 30

or, θ = 330°

therefore, the possible value of the angles in the principle branch would be 210 and 330 degrees.

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