Tutor profile: Thomas S.
NO CALC QUESTION Which of the following is equal to sin(π/6)? A) - sin(π/6) B) - cos(π/6) C) sin(π/3) D) cos(π/3)
In order to figure this one out, the most efficient way is the straight up know the rule, which is: sin(x) = cos(π/2 - x) Using this formula, we can plug in π/6 for x and find cos(π/2-π/6) now let's focus on the middle: π/2 - π/6 find common denominators for the fractions: 3π/6 - π/6 = 2π/6 = π/3 cos(π/3) is your answer let's think of another way we might be able to figure it out if we can't remember or don't know that formula. we certainly know the unit circle by the time we take the SAT, and the unit circle has π/6 as one of its points if we can think of the points on the unit circle and use it to our knowledge, we may know that sin(π/6) = 1/2 because the unit circle helps us remember that the x-coordinate is the cosine value and the y-coordinate is the sine value. the y-coordinate at π/6 is 1/2, so we can remember that π/3 is another point on the unit circle and that's part of our answer choices. using these choices and this knowledge, we can find each value and compare it to see which one is the correct answer eventually, we will find the same thing, that cos(π/3) = sin(π/6), D, is our answer
What is the slope of any line parallel to the line 6x + 3y = 10? A) 3 B) 1/2 C) 2 D) -2 E) -1/2
equation of a line: y = mx + b where m is slope and b is y-intercept what does it mean to be parallel? parallel lines are two straight lines in a plane that do not intersect what does that mean in terms of the equation? if they do not intersect, they must have the same slope, so to answer this question, we need to know the slope of the original line in order to find the slope of any line parallel to it equation of the line: 6x + 3y = 10 solve for y to put in y-intercept form: 3y = 10 - 6x now we can divide: y = 10/3 - (6/3)x let's rewrite the equation so the x is in front and it's easier to clearly see the slope: y = - (6/3) x + 10/3 the slope, m, is equal to = -(6/3) = - 6 divided by 3 = -2, which is D because the slope of our original equation is -2, any line parallel to it would have the same slope, so the correct response is D
Simplify the expression: x + 3(2x-5) + 4y - 2(2x-y) + 3(5 - 2y-x)
distribute to the parentheses: x + 3*2x - 3*5 + 4y - 2*2x -2*-y + 3*5 + 3*-2y + 3*-x perform the multiplication: x + 6x - 15 + 4y - 4x + 2y + 15 - 6y - 3x combine like terms: 7x - 15 + 4y - 4x + 2y + 15 - 6y - 3x all x terms: 7x - 4x - 3x = 7x - 7x = 0 all y terms: 4y + 2y - 6y = 6y - 6y = 0 all constant terms: -15 + 15 = 0 add everything together: 0 + 0 + 0 = 0 your final answer = 0
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