Find the value for sin(θ) if the following conditions hold: cos(2 theta) = 3/4 and 270 degrees

sin(θ) = - 0.35355

Step-by-step explanation:

The second condition is

270 degrees<theta<360 degrees

cos(2*theta) = 3/4  

And we know the relation

cos(2*θ)=1-2sin^2(θ)

This means that,

sin^2(θ) = 0.5*(1-cos(2*θ))

sin(θ) = ± √(0.5*(1-cos(2*θ)))

sin(θ) = ± √ (0.125)

sin(θ) = ± 0.35355

But we are in the 4th quadrant.

This means that the sine is negative.

sin(θ) = - 0.35355

=====================================

explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

29.5977692753

step-by-step explanation: