I got tan
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#3
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brandolf (06/03/2015) [-] 
As a math nerd and grad student in physics, this made my day better. Thank you, good sir.
#6 to #5
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brandolf (06/04/2015) [-] I'd love to help. It's what I do.
I assume you mean "find the angle for which cos(θ) = -1". For this the angle would be θ=180°. For "find the angle for which sin(θ) = sqrt(3)/2", the angle would be θ = 30°. The only real ways to find these angles for a given sine or cosine value is to use the inverse of the function on a scientific calculator, or just memorize the unit circle. Sine and cosine are the ratios of the lengths of the short sides of a right triangle to the length of the long side, or hypotenuse.
Sin(θ) = (length of the opposite side)/(length of the hypotenuse)
Cos(θ) = (length of the adjacent side)/(length of the hypotenuse)
Tan(θ) = (length of the opposite side)/(length of the adjacent side)
Are you familiar with the unit circle? Notice you only have to memorize the first quadrant (from zero to ninety degrees) and the other three are various negatives of the values. The radius of the circle on this is 1. Since the hypotenuse length is set to length 1, the ordered pairs in the image are the (x,y) coordinates of the point on the radius of the circle with the hypotenuse at the given angle.
I know this ain't easy, but I'll help however I can.
I assume you mean "find the angle for which cos(θ) = -1". For this the angle would be θ=180°. For "find the angle for which sin(θ) = sqrt(3)/2", the angle would be θ = 30°. The only real ways to find these angles for a given sine or cosine value is to use the inverse of the function on a scientific calculator, or just memorize the unit circle. Sine and cosine are the ratios of the lengths of the short sides of a right triangle to the length of the long side, or hypotenuse.
Sin(θ) = (length of the opposite side)/(length of the hypotenuse)
Cos(θ) = (length of the adjacent side)/(length of the hypotenuse)
Tan(θ) = (length of the opposite side)/(length of the adjacent side)
Are you familiar with the unit circle? Notice you only have to memorize the first quadrant (from zero to ninety degrees) and the other three are various negatives of the values. The radius of the circle on this is 1. Since the hypotenuse length is set to length 1, the ordered pairs in the image are the (x,y) coordinates of the point on the radius of the circle with the hypotenuse at the given angle.
I know this ain't easy, but I'll help however I can.
