Buy a calculator? lol jk
I assume you mean 4cos(330 degrees)-3tg(330degrees) cause it's badly worded.
Anyways, 330 degrees is 270+60 degree's, or 360-30 degrees. If you visualise it, it's three quarters of a pie plus 60 degrees, or a whole pie minus 30 degrees. (Draw with me if you want to understand)
The cosinus is the one where you draw a line to the x-axis. If you draw your line firther to the other side of the circle, you'll end up in 30 degrees. (Which makes sense, since cos(-x) = cos(x). And the cosinus of 30 degrees is? Indeed, square root of 3 divided by 2.
Then the tangens. That's when you draw a vertical line through the 1 on the x-axis, and look where that line intersects with your line from your 330 degrees. Or, the tangens is the sinus divided by the cosinus of the degree. The cosinus we allready calculated is sqrt(3)/2. The sinus of 330 is going to the left after you intersect with the circle (with radius 1). If you do this, you'll immediately see that sin(330) = - sin(30). And sin 30 is 1/2. So the tangens is (1/2) / (sqrt(3)/2) = 1/sqrt(3)
Soo we have: 4cos(330 degrees)-3tg(330degrees) = 4*sqrt(3)/2 - 3*(1/sqrt(3))
For 210 and 240 degrees, you follow the same process:
210 = 180 + 30, so you'll have half a pie plus 30 degrees. The tangens means extending the line, so
tan(210)= - tan(30)
240 = 180 + 60 and we see sin(240) = go to y-axis = same as minus 90+60 degrees, which is the same as sin 60, so sin(240) = - sin (60).
Hope I helped :O
I assume you mean 4cos(330 degrees)-3tg(330degrees) cause it's badly worded.
Anyways, 330 degrees is 270+60 degree's, or 360-30 degrees. If you visualise it, it's three quarters of a pie plus 60 degrees, or a whole pie minus 30 degrees. (Draw with me if you want to understand)
The cosinus is the one where you draw a line to the x-axis. If you draw your line firther to the other side of the circle, you'll end up in 30 degrees. (Which makes sense, since cos(-x) = cos(x). And the cosinus of 30 degrees is? Indeed, square root of 3 divided by 2.
Then the tangens. That's when you draw a vertical line through the 1 on the x-axis, and look where that line intersects with your line from your 330 degrees. Or, the tangens is the sinus divided by the cosinus of the degree. The cosinus we allready calculated is sqrt(3)/2. The sinus of 330 is going to the left after you intersect with the circle (with radius 1). If you do this, you'll immediately see that sin(330) = - sin(30). And sin 30 is 1/2. So the tangens is (1/2) / (sqrt(3)/2) = 1/sqrt(3)
Soo we have: 4cos(330 degrees)-3tg(330degrees) = 4*sqrt(3)/2 - 3*(1/sqrt(3))
For 210 and 240 degrees, you follow the same process:
210 = 180 + 30, so you'll have half a pie plus 30 degrees. The tangens means extending the line, so
tan(210)= - tan(30)
240 = 180 + 60 and we see sin(240) = go to y-axis = same as minus 90+60 degrees, which is the same as sin 60, so sin(240) = - sin (60).
Hope I helped :O