Chapter 4 Test
evaluate sin13pi/6
13pi/6 makes 2 complete rotations, and then there's just pi/6 look at unit circle and see that sin pi/6 = 1/2
supplementary angles add up to
180
What is 40.75° in DMS
2nd, angle, DMS
sine and cosine have a period of
2pi
find cos(100pi)
2pi is one revolution so it goes around 50 times but comes back to 0 cos(0)=1
how many radians are in 360°
2pi radians
31°5'6'' by hand
31+(5/60)+(6/3600)
31°5'6'' on a calculator
31, 2nd, apps, ⁰ 5, 2nd, apps, '
330°25"
330 + (1/3600)
1 radian in degrees
57°
complementary angles add up to
90
cos(t)
x
cot(t)
x/y
sin(t)
y
tan(t)
y/x
Whats the inverse of√2/2, rationalized
√2
how do you do radians to degrees
* (pi/180)
Find two angles that are coterminal with pi/6
-11pi/6 13pi/6
How do you find sec on a calculator
1/cos
sec(t)
1/x
csc(t)
1/y
s= 4 inches θ= 60° find r
REMEMBER-θ must be in radians 60 degrees = pi/3 radians 4=(pi/3)r
See the last problem on 4-3 right triangle trig notes
SERIOUSLY
How do you find a coterminal angle
add or subtract 2pi
coterminal angle
angles that have the same initial and terminal side
A merry go round goes 1 revolution/ 4 seconds outside has 20 ft radius whats linear and angular speed
angular speed: 2pi radians/ 4 sec 1.57 radians/sec Linear speed: (20 feet * 2pi radians)/ 4 seconds 31.4 feet/second
Formula for angular speed
angular speed=θ/t so radians/second or radians/min
what does an even function mean
cos(pi/6)=cos(-pi/6) cos(pi/4)= √2/2 cos(-pi/4)= √2/2
sine corresponds to
cosecant
What functions are even
cosine and secant
Find 2 solutions 0≤θ≤2pi for which secθ=-1.75
cos⁻¹(1/-1.75) 2.18 Second solution: 2.18+2pi
use its period to find sin(63pi/6)
if you went around 60pi times, with one revolution being 2pi, that's 12 full revolutions. Then you go around another 3pi/6 times, or pi/2 So really you're just looking for sin(pi/2) sin(pi/2)=1
Formula for linear speed
linear speed= s/t remember that s=rθ so linear speed= rθ/t
Find cos (-47pi/3)
really finding cos (-5pi-3) -1/2
Find tan 19pi / 4
really finding tan(3pi/4)= -1
earth's radius is 6378. Distance between 2 cities is 450. What is angle measure?
s=ro 450=(6378)(θ) θ=.07055 .07055 radians* (180/pi) 4.04 degrees
In order to find sector area you need θ, so you might need to use
s=rθ
formula to find θ
s=rθ or θ=s/r same thing
cosine corresponds to
secant
tanθ=3, what are sin and cos
see page 277
You know what the triangle looks like. no height, first length is 13, second length is x 1st angle of elevation: 3.5 2nd angle of elevation: 9 What's h?
see work i guess
how do you solve a problem where you only have the hypotenuse of a 30 60 90 or 45 45 90 triangle and are asked to find the two sides use the unit circle if you need to remember the side length rules
set up a proportion use the unit circle if you need to remember the side length rules
evaluate sin, cos, tan 45 by making a trangle
sin and cos are √2/2 tan is 1
what does an odd function mean
sin(-pi/6)= -sin(pi/6)
evaluate sin, cos 60 and sin, cos 30 by making a trangle
sin60=√3/2 cos60=1/2 sin30= 1/2 cos30= √3/2
6 trig functions 5pi/4
sin= -√2/2 cos=-√2/2 tan= 1 csc= -√2 sec= -√2 cot=1
what are the six trigonometric functions for pi/6
sin=1/2 cos=√3/2 tan=√3/3 csc= 2 sec= (2√3)/3 cot=√3
What functions are odd
sine, cosecant, tangent, cotangent
pythagorean identity
sin²+cos²=1
right triangle, cosθ=0.8, what are sin and tan
sinθ= 0.6 tanθ= 0.75 see page 276
remember that tan=______ and cot=_______
tan= sin/cos cot= cos/sin
