Question

what is a simplified trigonometric expression for csc 0 sin 0-sin^2 0?
A.sec^20
B.cos^2 0
C.1-tan^2 0
D.tan0-sin^2 0

Answer 1

write everything in terms of sin and cos first

Answer 2

csc(a) = 1/sin(a)

Answer 3

For the function y=tan 0, which angle measure has the same value as 2pie/3?
A.5pie/3
B.7pie/6
C.4pie/3
D.pie/6

Answer 4

so you get

1 - sin^2(a)

Answer 5

and recall

sin^2 + cos^2 = 1

,

Answer 6

so, it is the same as cos^2(a)

Answer 7

remember the tangent has a period of pi

Answer 8

what are the period and amplitude of the function y=2sin4 0?
A.pie/2 and 2
B.pie and 4
C.pie /2 and 4
D.pie/2 and 1

Answer 9

add or subtract any multiple of pi

Answer 10

so 1 is B @DanJS

Answer 11

yeah, just have to rewrite csc as 1/sin instead, then you get 1 - sin^2

Answer 12

which is an identity, sin^2 + cos^2 = 1

Answer 13

is 2 B? @DanJS

Answer 14

tangent has a period of pi, rotation by pi will produce the same value

Answer 15

so A @DanJS

Answer 16

2/3 pi + pi

2/3 pi + 2pi
.
.
.

Answer 17

c @DanJS

Answer 18

yeah A works there, 2/3 pi + pi = 5/3 pi

Answer 19

tangent of 2/3 pi = tangent of 5/3 pi

try it

Answer 20

i though c cause 2*2 is 4 and the denominator stays the same @DanJS

Answer 21

not doubling the angle, adding pi to it. 3/3 pi

Answer 22

2/3 pi + 3/3 pi = 5/3 pi

Answer 23

none of the others work, keep adding pi

8/3 pi
11/3 pi

Answer 24

i see now okay next is 3 B @DanJS

Answer 25

y = 2*sin^4(a)

Answer 26

the amplitude is usually that number out front, A*sin(x), but here there is one difference

Answer 27

by how much does the mean of the data set below change if the outlier is removed? round your answer to the nearest tenth, if necessary.
8,6,9,12,19,7,10,8
A.0.5
B.0.6
C.1.3
D.2.4

Answer 28

sin(x) is always between -1 and 1

(sin(x))^4 is always possitive because of the even power, so sin^4(x) is between 0 and 1

Answer 29

so is it B. pie and 4 @DanJS

Answer 30

which one is the function

\[y = \sin^4(x)\]
or
\[y = \sin(4x)\]

Answer 31

what are the period and amplitude of the function y=2sin4 0?

A.pie/2 and 2
B.pie and 4
C.pie /2 and 4
D.pie/2 and 1

Answer 32

a @DanJS

Answer 33

is the 4 a power or part of the angle

Answer 34

the first power one, amplitude is 1 period is pi

second one is amplitude 2, period T=2pi/4 = pi/2

Answer 35

here is a little thing on the general form for trig function
http://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.754992.html

Answer 36

so its A @DanJS

Answer 37

but the 4 power keeps the sin function positive, so th eamplitude is not 2, it would be half of it, only positive values

Answer 38

if the function is y = 2*sin(4x) , not sin to the 4th power, then the answer is A yeah

Answer 39

c.pie/2 and4 @DanJS

Answer 40

if you have

y = A*sin(Bx)

the amplitude is A
the period is (2pi)/B

Answer 41

for y = 2*sin(4x)

period is (2pi)/4 or pi/2

amplitude is 2

Answer 42

a,b,c or d @DanJS