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I'm sorry, I really don't know what you mean by square root 3 and 1/2 of the hypotenuse.
If you have an angle that's -60 degrees, remember that graphing a negative angle means rotating clockwise past the horizontal (x) line. Looking at a clock, -60 degrees would be about where the 20 minute mark is (at the number 4).
-60° is in the 4rth quadrant and has a reference angle of 60° This means that this angle is coterminal with 300°. I believe the ordered pair is (1/2, √3/2).
A 45-45 triangle is a very special type of triangle, it has two congruent angles and two legs of the same length. The third angle is known because the angles of every triangle add to a total of 180 degrees, so if two angles are 45+45=90, then the third angle has to be 90. Check out this video, I hope it helps https://www.khanacademy.org/math/geometr…
If you have an angle that's -60 degrees, remember that graphing a negative angle means rotating clockwise past the horizontal (x) line. Looking at a clock, -60 degrees would be about where the 20 minute mark is (at the number 4).
-60° is in the 4rth quadrant and has a reference angle of 60° This means that this angle is coterminal with 300°. I believe the ordered pair is (1/2, √3/2).
A 45-45 triangle is a very special type of triangle, it has two congruent angles and two legs of the same length. The third angle is known because the angles of every triangle add to a total of 180 degrees, so if two angles are 45+45=90, then the third angle has to be 90. Check out this video, I hope it helps https://www.khanacademy.org/math/geometr…
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If the cosine is 60 degrees it is a special 30-60-90 triangle where the hypotenuse is twice the length of the adjacent side so the answer since cosine = adjacent side/hypotenuse = 1/2 < ---- answer
The sine is equally easy. Remember the definition of the sine is opposite side/hypotenuse. You already know the relationship of the adjacent side/hypotenuse so you can use Pythagoras to find the opposite side: Hypotenuse =2, adjacent side = 1
c^2 = a^2 + b^2
c^2 - a^2 = b^2
sqrt (c^2 - a^2) = b
sqrt (2^2 - 1^2) = b
sqrt(4 -1) = b
sqrt 3 = b
Since sine is opposite side/hypotenuse: sin (-30) = (sqrt3)/2 <----- answer
By the way the sign of the number has nothing to do with the trigonometric fraction.
check
(sqrt 3)/2 = 1.732/2 =.866
sin (-60) = .866
You are correct 225 is a 45 degree angle. One again you can determine the value with Pythagoras.
2^2 = a^2 + b^2, and since you have two 45 degree angles you know that it is an isosceles triangle so the two sides other than the hypotenuse are equal. thus a = b and by substitution:
2^2 = a^2 + a^2
4 = 2a^2
2 = a^2
sqrt2 = a
sin 45 = sqrt2/2
check sqrt 2/2 = .707
sin 45 = .707
cos 45 = .707
The sine is equally easy. Remember the definition of the sine is opposite side/hypotenuse. You already know the relationship of the adjacent side/hypotenuse so you can use Pythagoras to find the opposite side: Hypotenuse =2, adjacent side = 1
c^2 = a^2 + b^2
c^2 - a^2 = b^2
sqrt (c^2 - a^2) = b
sqrt (2^2 - 1^2) = b
sqrt(4 -1) = b
sqrt 3 = b
Since sine is opposite side/hypotenuse: sin (-30) = (sqrt3)/2 <----- answer
By the way the sign of the number has nothing to do with the trigonometric fraction.
check
(sqrt 3)/2 = 1.732/2 =.866
sin (-60) = .866
You are correct 225 is a 45 degree angle. One again you can determine the value with Pythagoras.
2^2 = a^2 + b^2, and since you have two 45 degree angles you know that it is an isosceles triangle so the two sides other than the hypotenuse are equal. thus a = b and by substitution:
2^2 = a^2 + a^2
4 = 2a^2
2 = a^2
sqrt2 = a
sin 45 = sqrt2/2
check sqrt 2/2 = .707
sin 45 = .707
cos 45 = .707
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that should help you. To do negative angles, instead of going counterclock wise, you go clock wise ^^
that should help you. To do negative angles, instead of going counterclock wise, you go clock wise ^^