Question

Given ( cos θ = -{3}{5} ) and ( θ ) lies in Quadrant II, find ( sin θ ). Enter your answer in the box.

a) ( {4}{5} )
b) ( -{4}{5} )
c) ( {3}{5} )
d) ( -{3}{5} )

Answer 1

For cos θ = -\frac{3}{5} in Quadrant II, the correct value of sin θ is found using the Pythagorean identity to be \frac{4}{5}. Therefore, the answer is a) ( \frac{4}{5} ).

Step-by-step explanation:

Given that cos θ = -\frac{3}{5} and θ lies in Quadrant II, to find sin θ, we recall that for any angle θ in any quadrant, the following identity holds true:

sin^2 θ + cos^2 θ = 1

This is one of the Pythagorean identities in trigonometry. Since we know cos θ, we can rearrange the identity to solve for sin θ:

sin^2 θ = 1 - cos^2 θ

sin^2 θ = 1 - (-\frac{3}{5})^2

sin^2 θ = 1 - \frac{9}{25}

sin^2 θ = \frac{16}{25}

Now, take the square root of both sides, remembering that sin θ can be positive or negative depending on the quadrant in which the angle lies. Since θ is in Quadrant II, where sine is positive, we have:

sin θ = \frac{4}{5}

Therefore, the correct answer is a) ( \frac{4}{5} ).