INVERSETRIGONOMETRIC

FUNCTIONSFOLDABLE & Card SORT

PRECALCULUS

INVERSE TRIGONOMETRIC FUNCTIONS

Here is an activity which will help your PreCalculus students with practice finding exact values of inverse trigonometric functions. The activity is designed as a puzzle sort and match. Students are given 24 puzzle pieces to match in sets of 4. Each set has an answer card and three expressions with the same value. An answer key is included. There is also a notebook style Foldable®, inspired by the work f Dinah Zike and used with permission, as a graphic organizer prior to the activity.

Teaching Suggestions:• Use the activity in groups • Use the activity as a review exercise prior to assessing students.

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Exact Values of Inverse Trig FunctionsDirections for Printing:

FOLDABLE

Step 1: Print pages front to back 1 & 2, 3 & 4. The the writing will face in opposite directions. This is an option on many printers as “ flip along the short side”.

Step 2: Cut the sheets in half along the 11” side. Each sheet will make two foldables.

Step 3:Line up the 2 pages so the tab labels are staggered as shown at right.

Step 4: Fold over the top portion of both pages and secure with a few staples at the top. The final product should look like this:

PUZZLE CARD SORTPrint each sheet of cards on a different color of card stock.

Cut all the cards apart to make one set. Laminate the cards for long lasting use.

Exact Values of Inverse

Trig Functions

Exact Values of Inverse

Trig Functions

© 2015 Flamingo MathTMJean Adams © 2015 Flamingo MathTMJean Adams

The Sine Function will be one-to-one if we

restrict the domain from _______________.

If you know the sine value, the inverse sine

function determines the ________________.

The sine function is _________ it has

______________ Symmetry.

Sine-Inverse Sine Identities

for ____________

for ____________

1sin (sin )x x− =

( )1sin sin x x− =

tan-1x

EX #3: Evaluate

A.

B.

C.

D.

E.

( )1tan 3− −

( )1tan 1−

( )1tan 0−

1 3tan tan

4π−

1 3tan tan

3−

tan-1x

EX #3: Evaluate

A.

B.

C.

D.

E.

( )1tan 3− −

( )1tan 1−

( )1tan 0−

1 3tan tan

4π−

1 3tan tan

3−

The Sine Function will be one-to-one if we

restrict the domain from _______________.

If you know the sine value, the inverse sine

function determines the ________________.

The sine function is _________ it has

______________ Symmetry.

Sine-Inverse Sine Identities

for ____________

for ____________

1sin (sin )x x− =

( )1sin sin x x− =

Another notation is arcsin xAnother notation is arcsin x

EX #1: Evaluate

A.

B.

C.

D.

E.

1 3sin

2−

1 1sin

2− −

( )1sin 5−

1 5sin sin

6π−

( )1sin sin 0.85−

EX #1: Evaluate

A.

B.

C.

D.

E.

1 3sin

2−

1 1sin

2− −

( )1sin 5−

1 5sin sin

6π−

( )1sin sin 0.85−

Sin-1x Sin-1x

The Tangent Function will be one-to-one if

we restrict the domain from ____________.

Like the sine function, the tangent

function has ________________ symmetry.

It is an ____________ function. Evaluating

inverse tangent problems mean we are

restricted to Quadrants ________________.

Tangent-Inverse Tangent Identities

for ____________

for ____________

1tan (tan )x x− =

( )1tan tan x x− =

The Tangent Function will be one-to-one if

we restrict the domain from ____________.

Like the sine function, the tangent

function has ________________ symmetry.

It is an ____________ function. Evaluating

inverse tangent problems mean we are

restricted to Quadrants ________________.

Tangent-Inverse Tangent Identities

for ____________

for ____________

1tan (tan )x x− =

( )1tan tan x x− =

Another notation is arctan x Another notation is arctan x

EX #2: Evaluate

A.

B.

C.

D.

E.

EX #2: Evaluate

A.

B.

C.

D.

E.

( )1cos 1− −

1 3cos

2−

( )1cos 0−

1 7cos cos

4π−

( )1cos cos 3.25−

cos-1x cos-1x

The Cosine Function will be one-to-one if

we restrict the domain from ____________.

When you know the cosine value, the

inverse cosine function determines the

angle . The cosine function is symmetric

with respect to the _________________. It is

an ______________ function.

Cosine-Inverse Cosine Identities

for ____________

for ____________

1cos (cos )x x− =

( )1cos cos x x− =

( )1cos 1− −

1 3cos

2−

( )1cos 0−

1 7cos cos

4π−

( )1cos cos 3.25−

The Cosine Function will be one-to-one if

we restrict the domain from ____________.

When you know the cosine value, the

inverse cosine function determines the

angle . The cosine function is symmetric

with respect to the _________________. It is

an ______________ function.

Cosine-Inverse Cosine Identities

for ____________

for ____________

1cos (cos )x x− =

( )1cos cos x x− =

Another notation is arccos x Another notation is arccos x

1 5sin cos

6π−

1 3csc cos

2−

−

1 1cot cos

2− − ( )1tan 1− −

1cos sin3π−

( )1cos cot 3−

3π

−sec3π

tan6π −

1 3tan tan

4π−

6π

1 1sin cos

2− −

1 2tan tan

3π−

2

1 1tan sin

2− − 4

π−

1 5sin cos

3π−

1sin tan 3−

1 3sin

2− −

( )1sec tan 3−

33

−1 5

sin cos4π−

( )1cot 3−32

1 2tan tan

3π−

1 5sin cos

6π−

3

π−

1 3sin

2− −

2( )1sec tan 3−

sec3π

1 3csc cos

2−

−

KEY

PU

ZZLE

# 1

KEY

PU

ZZLE

# 2

1 1cot cos

2− −

33

−1 1tan sin

2− −

tan6π −

4π

−1 3

tan tan4π−

1 5sin cos

4π−

( )1tan 1− −

KEY

PU

ZZLE

# 3

KEY

PU

ZZLE

# 4

1cos sin3π−

1 5sin cos

3π−

( )1cot 3−

6π

1 1sin cos

2− −

( )1cos cot 3−

32

1sin tan 3−

KEY

PU

ZZLE

# 5

KEY

PU

ZZLE

# 6

The Sine Function will be one-to-one if we

restrict the domain from _______________.

If you know the sine value, the inverse sine

function determines the ________________.

The sine function is _________ it has

______________ Symmetry.

Sine-Inverse Sine Identities

for ____________

for ____________

1sin (sin )x x− =

( )1sin sin x x− =

tan-1x

EX #3: Evaluate

A.

B.

C.

D.

E.

( )1tan 3− −

( )1tan 1−

( )1tan 0−

1 3tan tan

4π−

1 3tan tan

3−

tan-1x

EX #3: Evaluate

A.

B.

C.

D.

E.

( )1tan 3− −

( )1tan 1−

( )1tan 0−

1 3tan tan

4π−

1 3tan tan

3−

The Sine Function will be one-to-one if we

restrict the domain from _______________.

If you know the sine value, the inverse sine

function determines the ________________.

The sine function is _________ it has

______________ Symmetry.

Sine-Inverse Sine Identities

for ____________

for ____________

1sin (sin )x x− =

( )1sin sin x x− =

Another notation is arcsin xAnother notation is arcsin x

,2 2π π −

angleodd

origin

2 2xπ π

− ≤ ≤

1 1x− ≤ ≤

3π

−

4π

0

4π−

6π

EX #1: Evaluate

A.

B.

C.

D.

E.

1 3sin

2−

1 1sin

2− −

( )1sin 5−

1 5sin sin

6π−

( )1sin sin 0.85−

EX #1: Evaluate

A.

B.

C.

D.

E.

1 3sin

2−

1 1sin

2− −

( )1sin 5−

1 5sin sin

6π−

( )1sin sin 0.85−

Sin-1x Sin-1x

The Tangent Function will be one-to-one if

we restrict the domain from ____________.

Like the sine function, the tangent

function has ________________ symmetry.

It is an ____________ function. Evaluating

inverse tangent problems mean we are

restricted to Quadrants ________________.

Tangent-Inverse Tangent Identities

for ____________

for ____________

1tan (tan )x x− =

( )1tan tan x x− =

The Tangent Function will be one-to-one if

we restrict the domain from ____________.

Like the sine function, the tangent

function has ________________ symmetry.

It is an ____________ function. Evaluating

inverse tangent problems mean we are

restricted to Quadrants ________________.

Tangent-Inverse Tangent Identities

for ____________

for ____________

1tan (tan )x x− =

( )1tan tan x x− =

Another notation is arctan x Another notation is arctan x

3π

6π

−

undefined

6π

0.85

,2 2π π −

I & IV

oddorigin

2 2xπ π

− < <

x−∞ < < ∞

EX #2: Evaluate

A.

B.

C.

D.

E.

EX #2: Evaluate

A.

B.

C.

D.

E.

( )1cos 1− −

1 3cos

2−

( )1cos 0−

1 7cos cos

4π−

( )1cos cos 3.25−

cos-1x cos-1x

The Cosine Function will be one-to-one if

we restrict the domain from ____________.

When you know the cosine value, the

inverse cosine function determines the

angle . The cosine function is symmetric

with respect to the _________________. It is

an ______________ function.

Cosine-Inverse Cosine Identities

for ____________

for ____________

1cos (cos )x x− =

( )1cos cos x x− =

( )1cos 1− −

1 3cos

2−

( )1cos 0−

1 7cos cos

4π−

( )1cos cos 3.25−

The Cosine Function will be one-to-one if

we restrict the domain from ____________.

When you know the cosine value, the

inverse cosine function determines the

angle . The cosine function is symmetric

with respect to the _________________. It is

an ______________ function.

Cosine-Inverse Cosine Identities

for ____________

for ____________

1cos (cos )x x− =

( )1cos cos x x− =

Another notation is arccos x Another notation is arccos x

[ ]0,π

eveny-axis

0 x π≤ ≤

1 1x− ≤ ≤

π

6π

undefined

4π

4π

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