Few questions about Math [Precalculus]?

Question

1) If cos(t) = -3/5 and cot(t) >0, t is located in which quadrant? [ Please explain how you would know this]

2) Find a reference angle for Θ (theta) = 15pi/17

3) Find the domain, equation of the vertical asymptote, and y-intercept of the function with equation f(x) = log base 5(x+2)

4) Use the laws of logarithms to rewrite the expression: ln  fifth root of a^3 divided by xy^20

5) Given log base a 3 = 0.477 and log base a 2 = 0.301, find each of the following: accurate to 3 decimals.

log base a 6 = ?
log base a 1.5= ?
log base a 0.125= ?
log base a 3a = ?

Thanks a lot for any help.

Arin · Accepted Answer

1.) you need to know where the trig functions are positive and negitive. cos is negitive in the second and third quadrants, cot is postive in the first and third quadrants. so your answer would be the 3rd quadrant.

2.) Reference angle is the angle it makes with the x-axis. In this case 15pi/17 is about 159 degrees so we take 180 - 159 to get 21 degrees as a reference angle if you want exact answer then it would (pi - 15pi/17) = 2pi/17

3.) f(x) = log 5  (x+2) 
0 = log 5 (x+2)
x + 2 = 5^0
x + 2 = 1
x = -1 is your y-int
domain is x > -2 because you can't have log 0
Your vertical asymptote x = -2

4.) Log fifth root of a^3 / xy^20 
3/5 log a - log x - 20log y

5.) 
log a 6 = log a 3 + log a 2 = .778
log a 1.5 = log a 3 - log a 2 = .176
log a .125 = log a 1 - 3log a 2 = -.903
log a 3a = log a 3 + log a a = 1.477

cidyah · Answer

I have omitted writing base a. You can include it.
5) log(3) =0.477 log(2)=0.301
log(6) = log(3x2)=log(3)+log(2) (both to base a)
0.477+0.301=  0.778
b)log(1.5)=log(3/2)=log(3)-log(2) [ to base a]
=0.477-0.301=0.176
d)log(3a)=log(3)+log(a)=0.477+1=1.477
log(base a) a = 1

1) cos(t)=-3/5. cos() is negative in the 2nd and 3rd quadrant. 127 degrees.

hanstine · Answer

hi :)) For the 1st concern, you have the nicely suited formulation. you basically could desire to plug interior the values that are given. (3,0) are your x and y coordinates, that are interior the formulation. The linear equation y= 2x-3 could desire to be interior the final style that's y-2x+3=0. you have 1y-2x+3=0. A =one million, B=-2, and C=3. plug in all the values. you will get /one million(3) + -2(0) + 3/ throughout sq. root of (one million)^2 + (-2)^2. the respond could be 6/sq. root of five. Rationalize your answer, it may yield 6squareroot of five throughout 5. 2d query is easy. locate the slope of the line it extremely is perpendicular to y=one million/2x+one million. Slope = -2. y-one million=-2(x-(-3)). answer: y=-2x-5

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Few questions about Math [Precalculus]?

3 Answers