Question

Find the exact value of sin (theta) with cos(theta) = -3/4 and with its terminal side in Quadrant III.

a. 4/3

b. -7/4

c. -(sqrt 7)/4

d. (sqrt 7)/4

Answer 1

Actually, it does work out just fine with the values you have up there. If the cos of the angle is -3/4, and it is in the third quadrant, the value along the x axis is -3 and the hypotenuse is 4. Always positive. That means that we have to find the missing side using Pythagorean's Theorem.

$4^2-(-3)^2=b^2$ and

$16-9=b^2$ and

$b=\sqrt{7$.

If the side opposite the reference angle is the square root of 7, it is also negative because in the third quadrant both x and y are negative, so the sin of that angle will be $\frac{-\sqrt{7}}{4}$, choice c.

Answer 2

The exact value of sine of angle θ will be - (√7) / 4. Then the correct option is C.

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The value of the cosine of angle θ is negative 3/4 and with its terminal side in Quadrant III.

We know that sin² θ + cos² θ = 1

Then the value of the sine of angle θ will be

sin² θ + cos² θ = 1

sin² θ + (-3/4)² = 1

sin² θ + 9/16 = 1

sin² θ = 1 - 9/16

sin² θ = 7/16

sin θ = √(7/16)

sin θ = (√7) / 4

But we know that angle is in Quadrant III, then the value will be negative.

sin θ =  - (√7) / 4

The exact value of sine of angle θ will be - (√7) / 4.

Then the correct option is C.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

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