Question

If θ is an angle in standard position that terminates in Quadrant IV such that cosθ = 3/5, then cosθ/2 is:

a) (-√5)/5
b) (-2√2)/5
c) (-2√5)/5
d) (-4√5)/5

Answer 1

The value of cosθ/2 is (-2√2)/5.

Step-by-step explanation:

To find the value of cosθ/2, we can use the half-angle formula for cosine. The formula is given as:

cos(θ/2) = √((1+cosθ)/2)

In this case, we know that cosθ = 3/5. Substituting this value into the formula, we get:

cos(θ/2) = √((1+3/5)/2)

Simplifying, we have:

cos(θ/2) = √((8/5)/2)

cos(θ/2) = √(8/10)

cos(θ/2) = √8/√10

Therefore, the answer is option b) (-2√2)/5.