50 points and Brainliest! Help! ASAP ! If the sin 30° = 1 over 2 , then the cos 60° = . (1 point) A) 0, because the angles are complementary
B) 1 over 2, because the angles are complementary
C) square root 3 over 2, because the angles are complementary
D) 1, because the angles are complementary

B

Step-by-step explanation:

The angles are complementary. They add up to 90

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The sine is the opposite over the hypotenuse. This means that the opposite side to our 30 degree angle has a length of 1 and the hypotenuse has a length of 2.

Since we have angles of 30° and 60°, that means that this is a 30-60-90 triangle.

If you draw out this type of triangle triangle, you can see that the opposite side to the 30 degree angle (which has a length of 1) is the adjacent side to the 60 degree angle.

The cosine is equal to the adjacent over the hypotenuse, and we now know that the adjacent side to the sixty degree angle is 1 and we already know that the hypotenuse is 2, so this means that the cosine of sixty degrees is 1/2. This matches answer B) 1 over 2, because the angles are complementary. Complementary just means that the angles add up to 90 degrees (30+60=90). In trigonometry, the sine of a certain angle is equal to the cosine of that angle's complement.

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the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is