math test 3

how to find a reference angle

QI= the angle QII= 180-angle QIII= angle-180 QIV= 360-angle

the radian measure of an angle theta is the length of the _____ that subtends the angle in a circle of radius ___ to convert degrees to radians we multiply by to convert radians to degrees we multiply by

arc, 1 pi/180 180/pi

If we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the ______ point determined by t. What are the terminal points determined by 𝜋/2, 𝜋, −𝜋/2, and 2𝜋?

(0,1) (-1, 0) (0, -1) (1, 0)

Find t and the terminal point determined by t for each point in the figure, where t is increasing in increments of 𝜋/6 0 𝜋/6 𝜋/3 𝜋/2 2𝜋/3 5𝜋/6 𝜋 7𝜋/6 4𝜋/3 3𝜋/2 5𝜋/3 11𝜋/6 2𝜋

(1, 0) (sqrt3/2, 1/2) (1/2, sqrt3/2) (0, 1) (-1/2, sqrt3/2) (-sqrt3/2, 1/2) (-1, 0) (-sqrt3/2, -1/2) (-1/2, -sqrt3/2) (0, -1) (1/2, -sqrt3/2) (sqrt3/2, -1/2) (1, 0)

find the degree measure of the angle with the given radian measure -pi/15

-12 degrees

find the exact solution and the approximation of 4^3x+1=3^x-4

-2ln(18)/6ln(2)-ln(3) or -log(4)+4log(3)/3log(4)-log(3) -1.888965

most calculators can find logarithms with base ___ and base e. to find logarithms with different bases, you use the _________________. to find log3(6), we write ______________

change of base formula log(6)/log(3)

find the exact solution and approximation of e^-2x=8

-ln(8)/2 -1.039721

find the exact value of the trigonometric function cos(-7pi/6)

-sqrt3/2

the logarithm of a quotient of tow numbers is the same as the _________ of the logarithms of these numbers so log3(9/27)=

difference log3(9)-log3(27)

use a calculator to evaluate sec(17 degrees) tan(59 degrees)

1.04569 1.66428

use the law of logarithms to expand log3(sqrt3x^9/y)

1/2log3(3) + 9/2log3(x) - log3(y)

solve the logarithmic function 2log(x)=log(2)+log(6x-10)

10 and 2

A 18-ft ladder leans against a building so that the angle between the ground and the ladder is 66°. How high does the ladder reach on the building?

16

solve the logarithmic function log3(x)+log3(x+3)=log3(28)

4

Find the area of a triangle with the given description. (Round your answer to one decimal place.) a triangle with sides of length 10 and 25 and included angle 20°

42.8 formula is 1/2bh*sin theta

solve the logarithmic function log2(3)+log2(x)=log2(5)+log2(x-2)

5

find angle between 0degrees and 360degrees that is coterminal with the given angle. 420degrees

60degrees

a central angle theta in a circle of radius 2m is subtended by an arc of length 3m. find the measure of theta in degrees and radians

85.9 degrees 1.5 radians

true or false log(D+B) is the same as log(D)+log(B) log(DB) is the same as log(D)+log(B)

false true

use the law of logarithms to combine 4ln(2)+3ln(x)-1/2ln(x+4)

ln(16x^3/sqrt(x+4))

use the law of logarithms to expand ln(y*sqrt (x/z))

lny+1/2ln(x)-1/2ln(z)

use the laws of logarithms to combine 2log(x)-1/3log(x^2+1)+3log(x-1)

log(x^2(x-1)^3/ cube root (x^2+1))

for a triangle... sin(theta)= cos(theta)= tan(theta)= the trigonometric ratios do not depend on the size of the triangle. this is because all right triangles with the same acute angle theta are ____

oposite/hypotenuse adjacent/hypotenuse opposite/adjacent similar

the logarithm of a number raised to a power is the same as the ______ times the logarithm of the number so log3(9^6)=

power 6xlog3(9)

the sign of a trigonometric function of theta depends on the _______ in/on which the terminal side of the angle lies in Quandrant II, tan(theta) is in quadrant III, sin(theta) is in quadrant IV, tan (theta) is

quadrant negative for all

find the quadrant in which theta lies from the information given. sin(theta)<0 and cos(theta)>0

quadrant IV

find the radius r of the circle if an arc of length 8 m on the circle subtends a central angle 4pi/5 radians

r=3.18

what is the formula to find arc length

s=r*theta

if theta = pi/3, find the value of each expression sin(2theta) 4sin(theta)

sqrt3/2 2sqrt3

how do you find the distance between two cities

subtract the attitudes from each other and find the circumference of the earth s=theta/360 * C

the logarithm of a product of two numbers is the same as the _____ of the logarithms of these numbers so log4(16x64)=

sum log4(16)+log4(64)

if theta is in standard position, the the reference angle is the acute angle formed by the terminal side of theta and the _____. so the reference angle for theta=110 degrees=_____, and that for theta=190 degrees =_____ if theta is any angle, the value of the trigonometric function of theta is the same, except possibly for sign, as the value of the trigonometric function of the reference angle. so sin(110 dgerees)= Sin(___) and sin(190 degrees)= -sin(____)

x-axis , 70, 10 70, 10

find the solution of 11^(3x-4)=1/11

x=1

if a point lies on the unit circle and you have one coordinate of P what is the formula you use to find the other

x^2+y^2=1

Let P(x, y) be the terminal point on the unit circle determined by t. Then sin(t) = ____ cos(t)= _____ and tan(t)=_____

y, x, y/x