math help please

Question

Find an angle θ with 0∘<θ<360∘ that has the same:

Sine function value as 240∘

θ = Incorrect degrees

Cosine function value as 240∘

θ = Incorrect degrees

thank you for your time and help

Answer 1

Going back to the unit circle, remember that cos(θ) represents the x-value for a value on the circle and sin(θ) represents the y-value. So, reflect the angle across the x-axis and find your angle for the equivalent y-value, then do the same across the y-axis for the x-value. Hope this helps!

Answer 2

let x = theta

sin(240-x) = sin240cosx - cos240sinx = (-sqr3)/2)cosx - (-1/2)sinx= ((1-sinx) -(sqr3)cosx)/2

sines are positive in quadrants I and II

so for sin(240-x) to be = to another angle it would have to be an angle in the 1st two quadrants uf 0<249-x < 180

but an angle in quadrant III or IV, if 180<240-x<360

for example,

if x = 90, then 240-x = 240-90=150 and the other angle with same sine value = 30 degrees

sin(240-90) = sin30

in general sin(240-x) = (1/2)sinx - (sqr3)/2)cosx

sin(240-90) = sin150 =1/2

= (1/2)sin90 - (sqr3/2)cos90 = 1/2 - (sqr3/2)(0) = 1/2-0=1/2