Find the exact value by using a half-angle identity. cos five pi divided by twelve one divided by two times the square root of the quantity two plus the square root of three one divided by two times the square root of the quantity two minus the square root of three negative one divided by two times the square root of the quantity two plus the square root of three negative one divided by two times the square root of the quantity two minus the square root of three

+√[(2 - √3)/4]

Step-by-step explanation:

Here is the complete question

How do you find the exact values of cos(5pi/12) using the half angle formula?

Solution

The half-angle formula is

cos(θ/2) = ±√[(1 + cosθ)/2]

if cos(5π/12) = cos(θ/2) ⇒ θ/2 = 5π/12 ⇒ θ = 5π/6

So, θ = 5π/6 × 180/π = 150°

Cos150 = cos(180 - 30) = -cos30 = -cosπ/6 = -√3/2

So, cos(5π/12) = ±√[(1 + cos5π/6)/2]

= ±√[(1 + (-cosπ/6))/2]

= ±√[(1 - cosπ/6)/2]

= ±√[(1 - √3/2)/2]

= ±√[(2 - √3)/2 ÷ 2]

= ±√[(2 - √3)/4]

Since 5π/12 = 5π/12 × 180/π = 75° which is in the first quadrant, so

cos(5π/12) = +√[(2 - √3)/4]. We ignore the negative answer

answer is more than one

step-by-step explanation:

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.