Question 1

Write each expression in factored form as an algebraic expression of a single trigonometric function.
-$\cos x - \sin ^ { 2 } x - 1$

Accepted Answer

A)  $( \cos x + 2 ) ( \cos x - 1 )$ 
B)  $( \cot x + 1 ) ( \cot x - 1 )$ 
C)  $\cos ^ { 2 } x = 1$ 
D)  $\sin 2 x$ 
A)  $( \cos x + 2 ) ( \cos x - 1 )$ 
B)  $( \cot x + 1 ) ( \cot x - 1 )$ 
C)  $\cos ^ { 2 } x = 1$ 
D)  $\sin 2 x$

Question 2

Prove the identity.
-$$\frac { 1 - \sin t } { \cos t } = \frac { \cos t } { 1 + \sin t }$$

Accepted Answer

The answer of Prove the identity.
-\[\frac { 1 - \sin...

Question 3

Provide an appropriate response.
-Discuss the methods used to verify an identity and why you would choose a particular method.

Accepted Answer

There are several methods used to verify

Question 4

State whether the given measurements determine zero, one, or two triangles.
-$$\mathrm { A } = 43 ^ { \circ } , \mathrm { a } = 4 , \mathrm {~b} = 16$$

Accepted Answer

A)  Two 
B)  Zero 
C)  One 
A)  Two 
B)  Zero 
C)  One

Question 5

Without using the law of cosines, explain why it is impossible to construct a triangle with lengths $8.6 \mathrm {~cm} , 11.8$ $\mathrm { cm }$, and $21.9 \mathrm {~cm}$.

Accepted Answer

In any triangle, the sum of th

Question 6

Solve.
-Points $\mathrm { A }$ and $\mathrm { B }$ are on opposite sides of a lake. A point $\mathrm { C }$ is $89.2$ meters from $\mathrm { A }$. The measure of angle BAC is $75 ^ { \circ } 40 ^ { \prime }$, and the measure of angle $\mathrm { ACB }$ is determined to be $39 ^ { \circ } 30 ^ { \prime }$. Find the distance between points $\mathrm { A }$ and $\mathrm { B }$ (to the nearest meter).

Accepted Answer

A)  $30 \mathrm {~m}$ 
B)  $61 \mathrm {~m}$ 
C)  $32 \mathrm {~m}$ 
D)  $63 \mathrm {~m}$ 
A)  $30 \mathrm {~m}$ 
B)  $61 \mathrm {~m}$ 
C)  $32 \mathrm {~m}$ 
D)  $63 \mathrm {~m}$

Question 7

Find the area. Round your answer to the nearest hundredth if necessary.
-Find the area of the triangle with the following measurements:
$$\mathrm { B } = 63 ^ { \circ } , \mathrm { a } = 10 \mathrm {~cm} , \mathrm { c } = 22 \mathrm {~cm}$$

Accepted Answer

A)  $98.01 \mathrm {~cm} ^ { 2 }$ 
B)  $196.02 \mathrm {~cm} ^ { 2 }$ 
C)  $49.94 \mathrm {~cm} ^ { 2 }$ 
D)  $110 \mathrm {~cm} ^ { 2 }$ 
A)  $98.01 \mathrm {~cm} ^ { 2 }$ 
B)  $196.02 \mathrm {~cm} ^ { 2 }$ 
C)  $49.94 \mathrm {~cm} ^ { 2 }$ 
D)  $110 \mathrm {~cm} ^ { 2 }$

Question 8

Solve the triangle.
-

Accepted Answer

A)  $\mathrm { A } = 56.8 ^ { \circ } , \mathrm { B } = 74.4 ^ { \circ } , \mathrm { C } = 48.8 ^ { \circ }$ 
B)  $\mathrm { A } = 48.8 ^ { \circ } , \mathrm { B } = 56.8 ^ { \circ } , \mathrm { C } = 74.4 ^ { \circ }$ 
C)  $\mathrm { A } = 56.8 ^ { \circ } , \mathrm { B } = 48.8 ^ { \circ } , \mathrm { C } = 74.4 ^ { \circ }$ 
D)  $\mathrm { A } = 74.4 ^ { \circ } , \mathrm { B } = 48.8 ^ { \circ } , \mathrm { C } = 56.8 ^ { \circ }$ 
A)  $\mathrm { A } = 56.8 ^ { \circ } , \mathrm { B } = 74.4 ^ { \circ } , \mathrm { C } = 48.8 ^ { \circ }$ 
B)  $\mathrm { A } = 48.8 ^ { \circ } , \mathrm { B } = 56.8 ^ { \circ } , \mathrm { C } = 74.4 ^ { \circ }$ 
C)  $\mathrm { A } = 56.8 ^ { \circ } , \mathrm { B } = 48.8 ^ { \circ } , \mathrm { C } = 74.4 ^ { \circ }$ 
D)  $\mathrm { A } = 74.4 ^ { \circ } , \mathrm { B } = 48.8 ^ { \circ } , \mathrm { C } = 56.8 ^ { \circ }$

Question 9

Solve the triangle.
-$$a = 6 , b = 11 , c = 8$$

Accepted Answer

A)  $\mathrm { A } \approx 32.2 ^ { \circ } , \mathrm { B } \approx 102.6 ^ { \circ } , \mathrm { C } \approx 45.2 ^ { \circ }$ 
B)  $\mathrm { A } \approx 32.2 ^ { \circ } , \mathrm { B } \approx 105.6 ^ { \circ } , \mathrm { C } \approx 42.2 ^ { \circ }$ 
C)  No triangles possible 
D)  $A \approx 32.2 ^ { \circ } , B \approx 45.2 ^ { \circ } , C \approx 102.6 ^ { \circ }$ 
A)  $\mathrm { A } \approx 32.2 ^ { \circ } , \mathrm { B } \approx 102.6 ^ { \circ } , \mathrm { C } \approx 45.2 ^ { \circ }$ 
B)  $\mathrm { A } \approx 32.2 ^ { \circ } , \mathrm { B } \approx 105.6 ^ { \circ } , \mathrm { C } \approx 42.2 ^ { \circ }$ 
C)  No triangles possible 
D)  $A \approx 32.2 ^ { \circ } , B \approx 45.2 ^ { \circ } , C \approx 102.6 ^ { \circ }$

Question 10

Find the area. Round your answer to the nearest hundredth if necessary.
-A regular polygon with 8 sides is circumscribed about a circle of radius 9 inches. Find the area of the polygon.

Accepted Answer

A)  214.76 square inches 
B)  380.29 square inches 
C)  275.69 square inches 
D)  347.75 square inches 
A)  214.76 square inches 
B)  380.29 square inches 
C)  275.69 square inches 
D)  347.75 square inches

Question 11

Complete the identity.
-The expression $\frac { \sec x + \csc x } { \tan x + \cot x }$
is to be the left hand side of an equation that is an identity. Which one of the following four expressions can be u the right hand side of the equation to complete the identity?

Accepted Answer

A)  $\tan x - \sec x$ 
B)  $\sin x + \cos x$ 
C)  $\cot x + \sin ^ { 2 } x$ 
D)  $\cos x + 1$ 
A)  $\tan x - \sec x$ 
B)  $\sin x + \cos x$ 
C)  $\cot x + \sin ^ { 2 } x$ 
D)  $\cos x + 1$

Question 12

Simplify the expression to either 1 or -1.
-$\cot x \tan x$

Accepted Answer

A)  1 
B)  -1 
A)  1 
B)  -1

Question 13

Simplify the expression to either 1 or -1.
-csc (-x) sin (-x)

Accepted Answer

A)  -1 
B)  1 
A)  -1 
B)  1

Question 14

Find the exact value by using a half-angle identity.
-$\cos \frac { 5 \pi } { 12 }$

Accepted Answer

A)  $- \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$ 
B)  $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$ 
C)  $\frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$ 
D)  $- \frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$ 
A)  $- \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$ 
B)  $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$ 
C)  $\frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$ 
D)  $- \frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$

Question 15

Prove the identity.
-$$\cos 3 x = \cos ^ { 3 } x - 3 \sin ^ { 2 } x \cos x$$

Accepted Answer

\[\begin{array} { l } 
\cos 3 x = \cos (

Question 16

Decide whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the
triangle.
-a = 240 b = 126
C = 327

Accepted Answer

A)  12,596.45 
B)  No triangle is formed. 
C)  29,453.71 
D)  29,439.61 
A)  12,596.45 
B)  No triangle is formed. 
C)  29,453.71 
D)  29,439.61

Question 17

Determine if the following is an identity.
-$\cos x \csc x \tan x = 1$

Accepted Answer

A)  Identity 
B)  Not an identity 
A)  Identity 
B)  Not an identity

Question 18

Prove the identity.
-$$\frac { \cot ^ { 2 } x } { \csc x - 1 } = \frac { 1 + \sin x } { \sin x }$$

Accepted Answer

The answer of Prove the identity.
-\[\frac { \cot ^ {...

Question 19

Use the fundamental identities to find the value of the trigonometric function.
-Given that $\tan \left( \theta - \frac { \pi } { 2 } \right) = - 0.4$, find $\cot \theta$.

Accepted Answer

A)  $2.5$ 
B)  $- 0.4$ 
C)  $0.4$ 
D)  $- 2.5$ 
A)  $2.5$ 
B)  $- 0.4$ 
C)  $0.4$ 
D)  $- 2.5$

Question 20

Write each expression in factored form as an algebraic expression of a single trigonometric function.
-$\sec ^ { 4 } x + \sec ^ { 2 } x \tan ^ { 2 } x - 2 \tan ^ { 4 } x$

Accepted Answer

A)  $4 \sec ^ { 2 } x$ 
B)  $3 \sec ^ { 2 } x - 2$ 
C)  $\sec ^ { 2 } x + 2$ 
D)  $\tan ^ { 2 } x - 1$ 
A)  $4 \sec ^ { 2 } x$ 
B)  $3 \sec ^ { 2 } x - 2$ 
C)  $\sec ^ { 2 } x + 2$ 
D)  $\tan ^ { 2 } x - 1$

Write each expression in factored form as an algebraic expression of a single trigonometric function. - $\cos x - \sin ^ { 2 } x - 1$

Prove the identity. - $\frac { 1 - \sin t } { \cos t } = \frac { \cos t } { 1 + \sin t }$

Provide an appropriate response. -Discuss the methods used to verify an identity and why you would choose a particular method.

State whether the given measurements determine zero, one, or two triangles. - $\mathrm { A } = 43 ^ { \circ } , \mathrm { a } = 4 , \mathrm {~b} = 16$

Without using the law of cosines, explain why it is impossible to construct a triangle with lengths $8.6 \mathrm {~cm} , 11.8$ $\mathrm { cm }$ , and $21.9 \mathrm {~cm}$ .

Find the area. Round your answer to the nearest hundredth if necessary. -Find the area of the triangle with the following measurements: $\mathrm { B } = 63 ^ { \circ } , \mathrm { a } = 10 \mathrm {~cm} , \mathrm { c } = 22 \mathrm {~cm}$

Solve the triangle. -

Solve the triangle. - $a = 6 , b = 11 , c = 8$

Find the area. Round your answer to the nearest hundredth if necessary. -A regular polygon with 8 sides is circumscribed about a circle of radius 9 inches. Find the area of the polygon.

Complete the identity. -The expression $\frac { \sec x + \csc x } { \tan x + \cot x }$ is to be the left hand side of an equation that is an identity. Which one of the following four expressions can be u the right hand side of the equation to complete the identity?

Simplify the expression to either 1 or -1. - $\cot x \tan x$

Simplify the expression to either 1 or -1. -csc (-x) sin (-x)

Find the exact value by using a half-angle identity. - $\cos \frac { 5 \pi } { 12 }$

Prove the identity. - $\cos 3 x = \cos ^ { 3 } x - 3 \sin ^ { 2 } x \cos x$

Decide whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. -a = 240 b = 126 C = 327

Determine if the following is an identity. - $\cos x \csc x \tan x = 1$

Prove the identity. - $\frac { \cot ^ { 2 } x } { \csc x - 1 } = \frac { 1 + \sin x } { \sin x }$

Use the fundamental identities to find the value of the trigonometric function. -Given that $\tan \left( \theta - \frac { \pi } { 2 } \right) = - 0.4$ , find $\cot \theta$ .

Write each expression in factored form as an algebraic expression of a single trigonometric function. - $\sec ^ { 4 } x + \sec ^ { 2 } x \tan ^ { 2 } x - 2 \tan ^ { 4 } x$

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Exam 5: Analytic Trigonometry

Write each expression in factored form as an algebraic expression of a single trigonometric function. - cos⁡x−sin⁡2x−1\cos x - \sin ^ { 2 } x - 1cosx−sin2x−1

Prove the identity. - 1−sin⁡tcos⁡t=cos⁡t1+sin⁡t\frac { 1 - \sin t } { \cos t } = \frac { \cos t } { 1 + \sin t }cost1−sint​=1+sintcost​