Let a be an angle, with 0≤α<2π0≤α<2π. Given cos(2α)=17/49 and 2α is in quadrant IV, find exact values of the six trigonometric functions.

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Let a be an angle, with 0≤α<2π0≤α<2π. Given cos(2α)=17/49 and 2α is in quadrant IV, find exact values of the six trigonometric functions.

tan(theta) = y/x = 2/1 = 2

sin(theta) = y/r = 2/√5

cos(theta) = x/r = 1/√5

tan(theta) = y/x = -2/√5

sin(theta) = y/r = -2/-1 = 2

cos(theta) = x/r = -1/√5

Step-by-step explanation:

-2x+y =0

y = 2x

So the ratio between y to x is:

y/x = 2

y:x = 2:1

For example, if x = 1, y = 2. Using this we'll get the hypotenus or the length of the terminal side as below

r = √(1^2 + 2^2) = √5

So the trigo for these are:

tan(theta) = y/x = 2/1 = 2

sin(theta) = y/r = 2/√5

cos(theta) = x/r = 1/√5

Another 3 trigo is when both x and y is negative (3rd quadrant)

Ex: x=-1, y=-2

r will be √5 as well

Hence

tan(theta) = y/x = -2/√5

sin(theta) = y/r = -2/-1 = 2

cos(theta) = x/r = -1/√5