<< Chapter < Page Chapter >> Page >

If tan t = 12 5 , and 0 t < π 2 , find sin t , cos t , sec t , csc t , and cot t .

Got questions? Get instant answers now!

If sin t = 3 2 and cos t = 1 2 , find sec t , csc t , tan t , and cot t .

sec t = 2 , csc t = 2 3 3 ,   tan t = 3 ,   cot t = 3 3

Got questions? Get instant answers now!

If sin 40° 0.643 and cos 40° 0.766 , find sec 40° , csc 40° , tan 40° , and cot 40° .

Got questions? Get instant answers now!

If sin t = 2 2 , what is the sin ( t ) ?

2 2

Got questions? Get instant answers now!

If cos t = 1 2 , what is the cos ( t ) ?

Got questions? Get instant answers now!

If sec t = 3.1 , what is the sec ( t ) ?

3.1

Got questions? Get instant answers now!

If csc t = 0.34 , what is the csc ( t ) ?

Got questions? Get instant answers now!

If tan t = −1.4 , what is the tan ( t ) ?

1.4

Got questions? Get instant answers now!

If cot t = 9.23 , what is the cot ( t ) ?

Got questions? Get instant answers now!

Graphical

For the following exercises, use the angle in the unit circle to find the value of the each of the six trigonometric functions.

This is an image of a graph of circle with angle of t inscribed. Point of (square root of 2 over 2, square root of 2 over 2) is at intersection of terminal side of angle and edge of circle.

sin t = 2 2 , cos t = 2 2 , tan t = 1 , cot t = 1 , sec t = 2 , csc t = 2

Got questions? Get instant answers now!

This is an image of a graph of circle with angle of t inscribed. Point of (-1/2, negative square root of 3 over 2) is at intersection of terminal side of angle and edge of circle.

sin t = 3 2 , cos t = 1 2 , tan t = 3 , cot t = 3 3 , sec t = 2 , csc t = 2 3 3

Got questions? Get instant answers now!

Technology

For the following exercises, use a graphing calculator to evaluate to three decimal places.

Extensions

For the following exercises, use identities to evaluate the expression.

If tan ( t ) 2.7 , and sin ( t ) 0.94 , find cos ( t ) .

Got questions? Get instant answers now!

If tan ( t ) 1.3 , and cos ( t ) 0.61 , find sin ( t ) .

sin ( t ) 0.79

Got questions? Get instant answers now!

If csc ( t ) 3.2 , and cos ( t ) 0.95 , find tan ( t ) .

Got questions? Get instant answers now!

If cot ( t ) 0.58 , and cos ( t ) 0.5 , find csc ( t ) .

csc t 1.16

Got questions? Get instant answers now!

Determine whether the function f ( x ) = 2 sin x cos x is even, odd, or neither.

Got questions? Get instant answers now!

Determine whether the function f ( x ) = 3 sin 2 x cos x + sec x is even, odd, or neither.

even

Got questions? Get instant answers now!

Determine whether the function f ( x ) = sin x 2 cos 2 x is even, odd, or neither.

Got questions? Get instant answers now!

Determine whether the function f ( x ) = csc 2 x + sec x is even, odd, or neither.

even

Got questions? Get instant answers now!

For the following exercises, use identities to simplify the expression.

sec t csc t

sin t cos t = tan t

Got questions? Get instant answers now!

Real-world applications

The amount of sunlight in a certain city can be modeled by the function h = 15 cos ( 1 600 d ) , where h represents the hours of sunlight, and d is the day of the year. Use the equation to find how many hours of sunlight there are on February 10, the 42 nd day of the year. State the period of the function.

Got questions? Get instant answers now!

The amount of sunlight in a certain city can be modeled by the function h = 16 cos ( 1 500 d ) , where h represents the hours of sunlight, and d is the day of the year. Use the equation to find how many hours of sunlight there are on September 24, the 267th day of the year. State the period of the function.

13.77 hours, period: 1000 π

Got questions? Get instant answers now!

The equation P = 20 sin ( 2 π t ) + 100 models the blood pressure, P , where t represents time in seconds. (a) Find the blood pressure after 15 seconds. (b) What are the maximum and minimum blood pressures?

Got questions? Get instant answers now!

The height of a piston, h , in inches, can be modeled by the equation y = 2 cos x + 6 , where x represents the crank angle. Find the height of the piston when the crank angle is 55° .

7.73 inches

Got questions? Get instant answers now!

The height of a piston, h , in inches, can be modeled by the equation y = 2 cos x + 5 , where x represents the crank angle. Find the height of the piston when the crank angle is 55° .

Got questions? Get instant answers now!

Chapter review exercises

Angles

For the following exercises, convert the angle measures to degrees.

For the following exercises, convert the angle measures to radians.

Find the length of an arc in a circle of radius 7 meters subtended by the central angle of 85° .

10.385 meters

Got questions? Get instant answers now!

Questions & Answers

f(x)=x/x+2 given g(x)=1+2x/1-x show that gf(x)=1+2x/3
Ken Reply
proof
AUSTINE
sebd me some questions about anything ill solve for yall
Manifoldee Reply
how to solve x²=2x+8 factorization?
Kristof Reply
x=2x+8 x-2x=2x+8-2x x-2x=8 -x=8 -x/-1=8/-1 x=-8 prove: if x=-8 -8=2(-8)+8 -8=-16+8 -8=-8 (PROVEN)
Manifoldee
x=2x+8
Manifoldee
×=2x-8 minus both sides by 2x
Manifoldee
so, x-2x=2x+8-2x
Manifoldee
then cancel out 2x and -2x, cuz 2x-2x is obviously zero
Manifoldee
so it would be like this: x-2x=8
Manifoldee
then we all know that beside the variable is a number (1): (1)x-2x=8
Manifoldee
so we will going to minus that 1-2=-1
Manifoldee
so it would be -x=8
Manifoldee
so next step is to cancel out negative number beside x so we get positive x
Manifoldee
so by doing it you need to divide both side by -1 so it would be like this: (-1x/-1)=(8/-1)
Manifoldee
so -1/-1=1
Manifoldee
so x=-8
Manifoldee
SO THE ANSWER IS X=-8
Manifoldee
so we should prove it
Manifoldee
x=2x+8 x-2x=8 -x=8 x=-8 by mantu from India
mantu
lol i just saw its x²
Manifoldee
x²=2x-8 x²-2x=8 -x²=8 x²=-8 square root(x²)=square root(-8) x=sq. root(-8)
Manifoldee
I mean x²=2x+8 by factorization method
Kristof
I think x=-2 or x=4
Kristof
x= 2x+8 ×=8-2x - 2x + x = 8 - x = 8 both sides divided - 1 -×/-1 = 8/-1 × = - 8 //// from somalia
Mohamed
1KI POWER 1/3 PLEASE SOLUTIONS
Prashant Reply
hii
Amit
how are you
Dorbor
well
Biswajit
can u tell me concepts
Gaurav
Find the possible value of 8.5 using moivre's theorem
Reuben Reply
which of these functions is not uniformly cintinuous on (0, 1)? sinx
Pooja Reply
which of these functions is not uniformly continuous on 0,1
Basant Reply
solve this equation by completing the square 3x-4x-7=0
Jamiz Reply
X=7
Muustapha
=7
mantu
x=7
mantu
3x-4x-7=0 -x=7 x=-7
Kr
x=-7
mantu
9x-16x-49=0 -7x=49 -x=7 x=7
mantu
what's the formula
Modress
-x=7
Modress
new member
siame
what is trigonometry
Jean Reply
deals with circles, angles, and triangles. Usually in the form of Soh cah toa or sine, cosine, and tangent
Thomas
solve for me this equational y=2-x
Rubben Reply
what are you solving for
Alex
solve x
Rubben
you would move everything to the other side leaving x by itself. subtract 2 and divide -1.
Nikki
then I got x=-2
Rubben
it will b -y+2=x
Alex
goodness. I'm sorry. I will let Alex take the wheel.
Nikki
ouky thanks braa
Rubben
I think he drive me safe
Rubben
how to get 8 trigonometric function of tanA=0.5, given SinA=5/13? Can you help me?m
Pab Reply
More example of algebra and trigo
Stephen Reply
What is Indices
Yashim Reply
If one side only of a triangle is given is it possible to solve for the unkown two sides?
Felix Reply
cool
Rubben
kya
Khushnama
please I need help in maths
Dayo Reply
Okey tell me, what's your problem is?
Navin
Practice Key Terms 6

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask