Question

given sin θ = -1/2 and angle θ is in quadrant IV, what is the exact value of cos θ in its simplest form

Answer 1

Answer:

Cos  θ = √3 / 2.

Step-by-step explanation:

The cosine si positive in quadrant IV.

Using the identity cos  θ = √(1 - sin^2 θ):

cos  θ = √(1 - (-1/2)^2)

= √ (3/4)

= √3 / 2

Answer 2

The cosine of theta will be evaluated as:

$cos(\theta) = \dfrac{\sqrt{3}}{2}$. It can be derived as shown below.

Given that:

sin(θ) = -1/2

Angle θ is in quadrant IV

To find: Value of cos(θ) in simplest form.

Calculations:

For angles belonging to quadrant IV, we have cos and sec trigonometric function evaluating positive result, and all others evaluate negative result on such angles.

Thus, we have:

$sin(\theta) = -1/2\\\theta = arcsin(\dfrac{-1}{2})\\\theta = - arcsin(\dfrac{1}{2})\\\theta = -30^\circ$

Thus, the cosine can be evaluated as:

$cos(\theta) = cos(-30) = cos(30) = \dfrac{\sqrt{3}}{2}$

Learn more about trigonometric functions here:

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