Question 1

Solve the triangle.
-

Accepted Answer

A)  $\mathrm { C } = 75 ^ { \circ } , \mathrm { c } \approx 4.2 , \mathrm { a } \approx 2.2$ 
B)  $\mathrm { C } = 15 ^ { \circ } , \mathrm { c } \approx 1.1 , \mathrm { a } \approx 2.2$ 
C)  $\mathrm { C } = 15 ^ { \circ } , \mathrm { c } \approx 3.8 , \mathrm { a } \approx 4.2$ 
D)  $\mathrm { C } = 75 ^ { \circ } , \mathrm { c } \approx 4.2 , \mathrm { a } \approx 3.8$ 
A)  $\mathrm { C } = 75 ^ { \circ } , \mathrm { c } \approx 4.2 , \mathrm { a } \approx 2.2$ 
B)  $\mathrm { C } = 15 ^ { \circ } , \mathrm { c } \approx 1.1 , \mathrm { a } \approx 2.2$ 
C)  $\mathrm { C } = 15 ^ { \circ } , \mathrm { c } \approx 3.8 , \mathrm { a } \approx 4.2$ 
D)  $\mathrm { C } = 75 ^ { \circ } , \mathrm { c } \approx 4.2 , \mathrm { a } \approx 3.8$

Question 2

Simplify the expression to either 1 or -1.
-sec (-x) cos (-x)

Accepted Answer

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

Question 3

Two triangles can be formed using the given measurements. Solve both triangles.
-$$\mathrm { A } = 58 ^ { \circ } , \mathrm { a } = 16 , \mathrm {~b} = 18$$

Accepted Answer

A)  $\mathrm { B } = 72.6 ^ { \circ } , \mathrm { C } = 49.4 ^ { \circ } , \mathrm { c } = 14.3 ; \mathrm { B } = 107.4 ^ { \circ } , \mathrm { C } = 14.6 ^ { \circ } , \mathrm { c } = 4.8$ 
B)  $\mathrm { B } = 17.4 ^ { \circ } , \mathrm { C } = 104.6 ^ { \circ } , \mathrm { C } = 18.3 ; \mathrm { B } = 162.6 ^ { \circ } , \mathrm { C } = 75.4 ^ { \circ } , \mathrm { c } = 18.3$ 
C)  $\mathrm { B } = 17.4 ^ { \circ } , \mathrm { C } = 104.6 ^ { \circ } , \mathrm { C } = 14 ; \mathrm { B } = 162.6 ^ { \circ } , \mathrm { C } = 75.4 ^ { \circ } , \mathrm { C } = 14$ 
D)  $\mathrm { B } = 72.6 ^ { \circ } , \mathrm { C } = 49.4 ^ { \circ } , \mathrm { c } = 17.9 ; \mathrm { B } = 107.4 ^ { \circ } , \mathrm { C } = 14.6 ^ { \circ } , \mathrm { c } = 17.9$ 
A)  $\mathrm { B } = 72.6 ^ { \circ } , \mathrm { C } = 49.4 ^ { \circ } , \mathrm { c } = 14.3 ; \mathrm { B } = 107.4 ^ { \circ } , \mathrm { C } = 14.6 ^ { \circ } , \mathrm { c } = 4.8$ 
B)  $\mathrm { B } = 17.4 ^ { \circ } , \mathrm { C } = 104.6 ^ { \circ } , \mathrm { C } = 18.3 ; \mathrm { B } = 162.6 ^ { \circ } , \mathrm { C } = 75.4 ^ { \circ } , \mathrm { c } = 18.3$ 
C)  $\mathrm { B } = 17.4 ^ { \circ } , \mathrm { C } = 104.6 ^ { \circ } , \mathrm { C } = 14 ; \mathrm { B } = 162.6 ^ { \circ } , \mathrm { C } = 75.4 ^ { \circ } , \mathrm { C } = 14$ 
D)  $\mathrm { B } = 72.6 ^ { \circ } , \mathrm { C } = 49.4 ^ { \circ } , \mathrm { c } = 17.9 ; \mathrm { B } = 107.4 ^ { \circ } , \mathrm { C } = 14.6 ^ { \circ } , \mathrm { c } = 17.9$

Question 4

Solve the problem.
-On a sunny day, a building and its shadow form the sides of a right triangle. If the hypotenuse is 36 m long and the shadow is 23 m, how tall is the building? (Round to the nearest tenth.)

Accepted Answer

A)  27.7 m 
B)  22.2 m 
C)  13.0 m 
D)  42.7 m 
A)  27.7 m 
B)  22.2 m 
C)  13.0 m 
D)  42.7 m

Question 5

Match the graph with the correct equation.
-

Accepted Answer

A)  y = sin x cos (-3) + cos x sin (-3) 
B)  y = sin x cos (-3) - cos x sin (-3) 
C)  y = cos x cos (-3) - sin x sin (-3) 
D)  y = cos x cos (-3) + sin x sin (-3) 
A)  y = sin x cos (-3) + cos x sin (-3) 
B)  y = sin x cos (-3) - cos x sin (-3) 
C)  y = cos x cos (-3) - sin x sin (-3) 
D)  y = cos x cos (-3) + sin x sin (-3)

Question 6

Determine if the following is an identity.
-$$\cot ^ { 2 } x = ( \csc x - 1 ) ( \csc x + 1 )$$

Accepted Answer

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

Question 7

Find all solutions in the interval [0, 2π).
-$$\tan \left( \frac { x } { 2 } \right) = \frac { 1 + \cos x } { 1 - \cos x }$$

Accepted Answer

A)  $\frac { \pi } { 4 } , \frac { 5 \pi } { 4 }$ 
B)  $\frac { \pi } { 2 }$ 
C)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
D)  0 
A)  $\frac { \pi } { 4 } , \frac { 5 \pi } { 4 }$ 
B)  $\frac { \pi } { 2 }$ 
C)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
D)  0

Question 8

Express the function as a sinusoid of the form y = a sin (bx + c).
-$$y = 7 \sin x + 5 \cos x$$

Accepted Answer

A)  $y = 74 \sin \left( x + \sin - 1 \left( \frac { 5 } { \sqrt { 74 } } \right) \right)$ 
B)  $y = \sqrt { 74 } \sin \left( x + \sin - 1 \left( \frac { 5 } { \sqrt { 74 } } \right) \right)$ 
C)  $y = 12 \sin ( 7 x + 5 )$ 
D)  $y = \sqrt { 74 } \sin \left( x + \cos - 1 \left( \frac { 5 } { \sqrt { 74 } } \right) \right\}$ 
A)  $y = 74 \sin \left( x + \sin - 1 \left( \frac { 5 } { \sqrt { 74 } } \right) \right)$ 
B)  $y = \sqrt { 74 } \sin \left( x + \sin - 1 \left( \frac { 5 } { \sqrt { 74 } } \right) \right)$ 
C)  $y = 12 \sin ( 7 x + 5 )$ 
D)  $y = \sqrt { 74 } \sin \left( x + \cos - 1 \left( \frac { 5 } { \sqrt { 74 } } \right) \right\}$

Question 9

Prove the identity.
-$$\frac { 1 - 2 \sec x - 3 \sec ^ { 2 } x } { - \tan ^ { 2 } x } = \frac { 1 - 3 \sec x } { 1 - \sec x }$$

Accepted Answer

The answer of Prove the identity.
-\[\frac { 1 - 2...

Question 10

Find an exact value.
-$\tan 75 ^ { \circ }$

Accepted Answer

A)  $2 + \sqrt { 3 }$ 
B)  $2 - \sqrt { 3 }$ 
C)  $- 2 + \sqrt { 3 }$ 
D)  $\frac { 2 + \sqrt { 3 } } { 4 }$ 
A)  $2 + \sqrt { 3 }$ 
B)  $2 - \sqrt { 3 }$ 
C)  $- 2 + \sqrt { 3 }$ 
D)  $\frac { 2 + \sqrt { 3 } } { 4 }$

Question 11

Find the area. Round your answer to the nearest hundredth if necessary.
-Find the area of the triangle with the following measurements: $C = 79 ^ { \circ } , a = 3.3$ in., $b = 5.8$ in.

Accepted Answer

A)  $18.79$ in. 2 
B)  $1.83$ in. 2 
C)  $9.39$ in. $^ { 2 }$ 
D)  $9.57$ in. $^ { 2 }$ 
A)  $18.79$ in. 2 
B)  $1.83$ in. 2 
C)  $9.39$ in. $^ { 2 }$ 
D)  $9.57$ in. $^ { 2 }$

Question 12

Prove the identity.
-$$\csc \left( \frac { \pi } { 2 } + u \right) = \sec u$$

Accepted Answer

@#LAT-DLM& Choose the one alte

Question 13

Determine if the following is an identity.
-$$\frac { \sin x } { 1 - \cos x } + \frac { \sin x } { 1 + \cos x } = 2 \csc x$$

Accepted Answer

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

Question 14

Provide an appropriate response.
-Graph the expression $\frac { 1 - \sin ^ { 2 } x } { \sin x - \csc x }$ on your calculator. Determine what constant or single circular function is equivalent to the given expression.

Accepted Answer

The answer of Provide an appropriate response.
-Graph the expression \(\frac...

Question 15

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is
formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.
-$$\mathrm { A } = 50 ^ { \circ } , \mathrm { a } = 9 , \mathrm {~B} = 63 ^ { \circ }$$

Accepted Answer

A)  $\mathrm { C } = 67 ^ { \circ } , \mathrm { b } \approx 10.5 , \mathrm { c } \approx 9.3$ 
B)  $\mathrm { C } = 23 ^ { \circ } , \mathrm { b } \approx 7.7 , \mathrm { c } \approx 9.3$ 
C)  $\mathrm { C } = 67 ^ { \circ } , \mathrm { b } \approx 10.5 , \mathrm { c } \approx 10.8$ 
D)  No triangle is formed. 
A)  $\mathrm { C } = 67 ^ { \circ } , \mathrm { b } \approx 10.5 , \mathrm { c } \approx 9.3$ 
B)  $\mathrm { C } = 23 ^ { \circ } , \mathrm { b } \approx 7.7 , \mathrm { c } \approx 9.3$ 
C)  $\mathrm { C } = 67 ^ { \circ } , \mathrm { b } \approx 10.5 , \mathrm { c } \approx 10.8$ 
D)  No triangle is formed.

Question 16

Find all solutions to the equation.
-$$\tan x = 3.7$$
(Use a calculator. Express your answer in radians, as a decimal rounded to the nearest thousandth.)

Accepted Answer

A)  $\{ 4.449 + 2 \mathrm { n } \pi , 4.976 + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \}$ 
B)  $\{ 1.835 + \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots . \}$ 
C)  $\{ 1.307 + 2 \mathrm { n } \pi , 1.835 + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \}$ 
D)  $\{ 1.307 + \mathrm { n } \pi | \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \rangle$ 
A)  $\{ 4.449 + 2 \mathrm { n } \pi , 4.976 + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \}$ 
B)  $\{ 1.835 + \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots . \}$ 
C)  $\{ 1.307 + 2 \mathrm { n } \pi , 1.835 + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \}$ 
D)  $\{ 1.307 + \mathrm { n } \pi | \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \rangle$

Question 17

Simplify the expression to either 1 or -1.
-$$\cos \left( \frac { \pi } { 2 } - x \right) \csc ( - x )$$

Accepted Answer

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

Question 18

Use basic identities to simplify the expression.
-$\frac { \tan \theta } { \sec \theta }$

Accepted Answer

A)  $\cos ^ { 3 } \theta$ 
B)  $\tan ^ { 2 } \theta$ 
C)  $\sin \theta$ 
D)  $\sec ^ { 2 } \theta$ 
A)  $\cos ^ { 3 } \theta$ 
B)  $\tan ^ { 2 } \theta$ 
C)  $\sin \theta$ 
D)  $\sec ^ { 2 } \theta$

Question 19

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 20

State whether the given measurements determine zero, one, or two triangles.
-$$\mathrm { C } = 35 ^ { \circ } , \mathrm { a } = 28 , \mathrm { c } = 30$$

Accepted Answer

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

Solve the triangle. -

Simplify the expression to either 1 or -1. -sec (-x) cos (-x)

Two triangles can be formed using the given measurements. Solve both triangles. - $\mathrm { A } = 58 ^ { \circ } , \mathrm { a } = 16 , \mathrm {~b} = 18$

Solve the problem. -On a sunny day, a building and its shadow form the sides of a right triangle. If the hypotenuse is 36 m long and the shadow is 23 m, how tall is the building? (Round to the nearest tenth.)

Match the graph with the correct equation. -

Determine if the following is an identity. - $\cot ^ { 2 } x = ( \csc x - 1 ) ( \csc x + 1 )$

Find all solutions in the interval [0, 2π). - $\tan \left( \frac { x } { 2 } \right) = \frac { 1 + \cos x } { 1 - \cos x }$

Express the function as a sinusoid of the form y = a sin (bx + c). - $y = 7 \sin x + 5 \cos x$

Prove the identity. - $\frac { 1 - 2 \sec x - 3 \sec ^ { 2 } x } { - \tan ^ { 2 } x } = \frac { 1 - 3 \sec x } { 1 - \sec x }$

Find an exact value. - $\tan 75 ^ { \circ }$

Find the area. Round your answer to the nearest hundredth if necessary. -Find the area of the triangle with the following measurements: $C = 79 ^ { \circ } , a = 3.3$ in., $b = 5.8$ in.

Prove the identity. - $\csc \left( \frac { \pi } { 2 } + u \right) = \sec u$

Determine if the following is an identity. - $\frac { \sin x } { 1 - \cos x } + \frac { \sin x } { 1 + \cos x } = 2 \csc x$

Provide an appropriate response. -Graph the expression $\frac { 1 - \sin ^ { 2 } x } { \sin x - \csc x }$ on your calculator. Determine what constant or single circular function is equivalent to the given expression.

Find all solutions to the equation. - $\tan x = 3.7$ (Use a calculator. Express your answer in radians, as a decimal rounded to the nearest thousandth.)

Simplify the expression to either 1 or -1. - $\cos \left( \frac { \pi } { 2 } - x \right) \csc ( - x )$

Use basic identities to simplify the expression. - $\frac { \tan \theta } { \sec \theta }$

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

State whether the given measurements determine zero, one, or two triangles. - $\mathrm { C } = 35 ^ { \circ } , \mathrm { a } = 28 , \mathrm { c } = 30$

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Exam 5: Analytic Trigonometry

Solve the triangle. -

Simplify the expression to either 1 or -1. -sec (-x) cos (-x)

Two triangles can be formed using the given measurements. Solve both triangles. - A=58∘,a=16, b=18\mathrm { A } = 58 ^ { \circ } , \mathrm { a } = 16 , \mathrm {~b} = 18A=58∘,a=16, b=18

Solve the problem. -On a sunny day, a building and its shadow form the sides of a right triangle. If the hypotenuse is 36 m long and the shadow is 23 m, how tall is the building? (Round to the nearest tenth.)

Match the graph with the correct equation. -

Determine if the following is an identity. - cot⁡2x=(csc⁡x−1)(csc⁡x+1)\cot ^ { 2 } x = ( \csc x - 1 ) ( \csc x + 1 )cot2x=(cscx−1)(cscx+1)

Find all solutions in the interval [0, 2π). - tan⁡(x2)=1+cos⁡x1−cos⁡x\tan \left( \frac { x } { 2 } \right) = \frac { 1 + \cos x } { 1 - \cos x }tan(2x​)=1−cosx1+cosx​

Express the function as a sinusoid of the form y = a sin (bx + c). - y=7sin⁡x+5cos⁡xy = 7 \sin x + 5 \cos xy=7sinx+5cosx

Prove the identity. - 1−2sec⁡x−3sec⁡2x−tan⁡2x=1−3sec⁡x1−sec⁡x\frac { 1 - 2 \sec x - 3 \sec ^ { 2 } x } { - \tan ^ { 2 } x } = \frac { 1 - 3 \sec x } { 1 - \sec x }−tan2x1−2secx−3sec2x​=1−secx1−3secx​

Find an exact value. - tan⁡75∘\tan 75 ^ { \circ }tan75∘

Find the area. Round your answer to the nearest hundredth if necessary. -Find the area of the triangle with the following measurements: C=79∘,a=3.3C = 79 ^ { \circ } , a = 3.3C=79∘,a=3.3 in., b=5.8b = 5.8b=5.8 in.

Prove the identity. - csc⁡(π2+u)=sec⁡u\csc \left( \frac { \pi } { 2 } + u \right) = \sec ucsc(2π​+u)=secu

Determine if the following is an identity. - sin⁡x1−cos⁡x+sin⁡x1+cos⁡x=2csc⁡x\frac { \sin x } { 1 - \cos x } + \frac { \sin x } { 1 + \cos x } = 2 \csc x1−cosxsinx​+1+cosxsinx​=2cscx

Provide an appropriate response. -Graph the expression 1−sin⁡2xsin⁡x−csc⁡x\frac { 1 - \sin ^ { 2 } x } { \sin x - \csc x }sinx−cscx1−sin2x​ on your calculator. Determine what constant or single circular function is equivalent to the given expression.

Find all solutions to the equation. - tan⁡x=3.7\tan x = 3.7tanx=3.7 (Use a calculator. Express your answer in radians, as a decimal rounded to the nearest thousandth.)

Simplify the expression to either 1 or -1. - cos⁡(π2−x)csc⁡(−x)\cos \left( \frac { \pi } { 2 } - x \right) \csc ( - x )cos(2π​−x)csc(−x)

Use basic identities to simplify the expression. - tan⁡θsec⁡θ\frac { \tan \theta } { \sec \theta }secθtanθ​

Prove the identity. - cot⁡2xcsc⁡x+1=1−sin⁡xsin⁡x\frac { \cot ^ { 2 } x } { \csc x + 1 } = \frac { 1 - \sin x } { \sin x }cscx+1cot2x​=sinx1−sinx​

State whether the given measurements determine zero, one, or two triangles. - C=35∘,a=28,c=30\mathrm { C } = 35 ^ { \circ } , \mathrm { a } = 28 , \mathrm { c } = 30C=35∘,a=28,c=30