Reciprocal Trigonometric Functions

An angle of a right triangle has a cotangent value of 5/12. Complete the statements using the given information and the diagram shown on the right.

a = 5 b = 12 c = 13

Find the exact value of sec(-135°).

-sqrt2

Simplify: sec(θ) sin(θ) cot(θ)

1

evaluate cot(pi/3)

sqrt3/3

What is the value of csc A in the triangle below?

sqrt337/16

to simplify a trigonometric function means _____

to write the expression as a numerical value

which function is undefined when theta = pi/2

tan theta

θ

theta

simplify cot(theta)sin(theta)

cos(theta)

simplify cot(theta)/cos(theta)

csc(merp)

what is the reference angle for 5pi/3

pi/3

select all that have negative values

csc(5pi/4) csc(340°) sec(120°)

Which are undefined?

sec(-pi/2) csc(3pi)

Which results from multiplying the six trigonometric functions?

1

inverse reciprocal trigonometric functions_____

can be used to find unknown angle measures

Simplify: cos(θ) csc(θ)/sin(θ) cot(θ)

csc(θ)

csc(theta) = 1/y, _____ sec(theta) = 1/x, _____ cot(theta) = x/y, _____

y not equal to 0 x not equal to 0 y not equal to 0

A 26-foot long ladder is leaning against a building at a 60° angle with the ground. Which of the following equations can you use to find the height of the building, h?

csc(60°) = 26/h

Select all that are undefined.

csc(pi) cot(pi) csc(0°) sec(90°)

the reciprocal trigonometric functions:

csc(theta) = 1/sin(theta) sec(theta) = 1/cos(theta) cot(theta) = 1/tan(theta) = cos(theta)/sin(theta)

to simplify reciprocal trigonometric functions:

rewrite in terms of sine and cosine and and write the expression as a numerical value, or in terms of a single trigonometric function if possible

Which of the following is a simpler form of the expression sin (theta)sec(theta)÷ cos(theta)tan(theta)

sec(theta)

find the six trigonometric values of 7pi/6

sin(pi/6) = 1/2 cos(pi/6) = 13/2 cos(merp) = -sqrt3/2 sin(merp) = -1/2 sec(merp) = -2sqrt3/3 csc(merp) = -2 tan(merp) = sqrt3/3 cot(merp) = sqrt3

to find the inverse of a reciprocal trigonometric function:

1. rewrite in terms of sine and cosine, using the reciprocal of the given value 2. find the angle measure

to evaluate reciprocal trigonometric functions:

1. locate the terminal side and find the reference angle 2. evaluate the sine, cosine, or tangent function of the reference angle 3. reciprocate the sine, cosine, or tangent value 4. attach the sign, positive or negative, based on the quadrant in which the angle terminates

What is the exact value of cos(-60º)?

1/2

sec(theta) = _____

13/5

what is sec(5pi/3)

2

What is the approximate height of the building? Round to the nearest tenth of a foot.

22.5

If tan theta = 11/60, what is the value of cot theta?

60/11

simplify sec(theta) cos (theta)

= 1/cos(theta) * cos(theta) = 1

Four students wrote statements about cosecant, secant, and cotangent values as shown below. Which student is correct?

Anik