In a 45-45-90 triangle, the two legs are congruent. Let's call them x. The hypotenuse is equal to 1 as we're using the unit circle. The hypotenuse of the triangle is the same as the radius of the unit circle.
a = x
b = x
c = 1
Use those values in the Pythagorean theorem to solve for x.
a^2 + b^2 = c^2
x^2 + x^2 = 1^2
2x^2 = 1
x^2 = 1/2
x = sqrt( 1/2 )
x = sqrt(1)/sqrt(2)
x = 1/sqrt(2)
x = sqrt(2)/2 ... rationalizing the denominator
So this right triangle has legs that are sqrt(2)/2 units long. Once we know the legs of the triangle, we can divide them over the hypotenuse to find the sine and cosine values.
sin(angle) = opposite/hypotenuse
sin(45) = (sqrt(2)/2) / 1
sin(45) = sqrt(2)/2
and
cos(angle) = adjacent/hypotenuse
cos(45) = (sqrt(2)/2) / 1
cos(45) = sqrt(2)/2
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For a 30-60-90 triangle, we would have
a = 1
b = x
c = 2
so,
a^2+b^2 = c^2
1^2+x^2 = 2^2
1+x^2 = 4
x^2 = 4-1
x^2 = 3
x = sqrt(3)
The missing leg is sqrt(3) units long.
Once we know the three sides of the 30-60-90 triangle, you should be able to see that
sin(30) = 1/2
sin(60) = sqrt(3)/2
cos(30) = sqrt(3)/2
cos(60) = 1/2
Answer:
i
Step-by-step explanation:
The equation is y=6x-5
y-intercept:
y=6(0) -5 = -5
so ordered pair for y intercept is (0,-5)
x-intercept:
0=6x-5
x=5/6
ordered pair for x-intercept is (5/6 , 0)
so the two ordered pairs are (0,-5) and (5/6,0)
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