Calc Ch.1 Review Round 2

Section 1.6

100

Find the missing arc length given that the angle measure is 5pi/8 and the radius is 5.

25pi/8

200

Give the measure of the angle in radians and degrees for tan^-1(-sqrt(3)/3) without using a calculator.

degrees: -30 or 330 

radians: -pi/6 or 5pi/6

300

Find the range of 5sin(2x + pi/4) - 2 without the calculator.

[-7,3]

400

Find all the trig values of theta if sin(theta) = 1/2 and tan(theta) < 0

sin(theta) = 1/2

cos(theta) = - sqrt(3)/2

tan(theta) = - sqrt(3)/3

csc(theta) = 2

sec(theta) = -2sqrt(3)/3

cot(theta) = -sqrt(3)

500

In a set of pool depth data, the deep end of a pool is 12 feet and the shallow end is 5 feet. What does that mean the amplitude of the pool depth is? 

amplitude is 3.5 feet

Fe Fi Fo(rmulas) Fum

100

_____ = y/r

sin(theta)

200

What is the formula for point intercept form?

y-y₁ = m(x - x₁)

300

If x and y are given as x = f(t) and y = g(t) over an interval of t values, then these equations are called what?

parametric equations

400

What is the formula for compound interest?

p(1 + (r/n))^nt

500

What is the general formula for a sinusoid?

f(x) = Asin[B(x - C)] + D

Let's get Triggy with It

100

When an angle measure theta is placed in standard position at the center of a circle with radius r, what is the equation for secant theta?

sec(theta) = r/x

200

-cos(30^o) = ____

sqrt(3)/2

300

What is the period for cotangent theta?

pi

400

What is the domain for y = csc^-1(x)?

|x| >= 1

500

What is the range of y = tan^-1(x)?

-pi/2 < y < pi/2

Let's have some Fun(ctions)

100

What are the three different methods we talked about for solving two linear equations simultaneously?

substitution, elimination, graphical

200

Is the following function even, odd, or neither. 

y = 3x³ - 2x² -1

neither

300

In words, when is a function one-to-one on domain D?

If f(a) doesn't equal f(b) whenever a doesn't equal b.

400

The half life of a certain radioactive substance is 8 hours. There are 5 grams present initially. When will there be 1 gram remaining?

18.6 years

500

What is the inverse of the function x² + 2x + 1 when x >= -1.

sqrt(y) - 1 = x

Random

100

What is the slope of the line x = 6.

undefined

200

What are the restricted and not restricted domains of functions called?

relevant and implied domains

300

What would be the Cartesian equation for the parametric curve x = sin(t), y = 7cos(t), 

0 <= t <= 2pi

x² + (y/7)² = 1

400

The result of composing a function and its inverse in either order is called a ________, the function that assigns each number to itself.

identity function

500

Who invented a symbolic way to say "y is a function of x" 

Euler