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

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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

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

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

2 2

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

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

3.1

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

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

1.4

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

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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

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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

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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 ) .

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

sin ( t ) 0.79

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

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

csc t 1.16

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

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

even

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

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

even

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

sec t csc t

sin t cos t = tan t

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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.

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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

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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?

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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

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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° .

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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

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Questions & Answers

write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
the polar co-ordinate of the point (-1, -1)
Sumit Reply
prove the identites sin x ( 1+ tan x )+ cos x ( 1+ cot x )= sec x + cosec x
Rockstar Reply
tanh`(x-iy) =A+iB, find A and B
Pankaj Reply
B=Ai-itan(hx-hiy)
Rukmini
what is the addition of 101011 with 101010
Branded Reply
If those numbers are binary, it's 1010101. If they are base 10, it's 202021.
Jack
extra power 4 minus 5 x cube + 7 x square minus 5 x + 1 equal to zero
archana Reply
the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
Practice Key Terms 6

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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