Question 1

Perform the calculation.
-$\cot \theta < 0$ and $\cos \theta > 0$
A) Quadrant III
B) Quadrant I
C) Quadrant II
D) Quadrant IV

Accepted Answer

In the fourth quadrant, $\cos \theta > 0$ and $\cot \theta = \frac{\cos \theta}{\sin \theta}$ is negative because $\sin \theta < 0$, making $\cot \theta < 0$.

Question 2

Place your graphing calculator in parametric and degree modes. Set the window for Tmin=0, Tmax=360, Tstep=1, Xmin= $- 1.8 , X _ { \max } = 1.8 , X _ { \text {scl } } = 1 , \mathrm { Y } _ { \min } = - 1.2 , \mathrm { Y } _ { \max } = 1.2 , \mathrm { Y } s \mathrm {~s} = 1$. Set the functions to $\mathrm { X } _ { 1 \mathrm {~T} } = \cos \mathrm { T } ^ { \mathrm { Y } } , \mathrm { Y } _ { 1 \mathrm {~T} } = \sin \mathrm { T }$. Graph the circle of radius 1 on the screen. Use the trace feature to move a short distance around the circle.
--116°
A)°
B)116°
C)244°
D)424

Accepted Answer

The answer of Place your graphing calculator in parametric and...

Question 3

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
-sec (-59°)and sin (-59°)
A)negative and positive
B)positive and positive
C)negative and negative
D)positive and negative

Accepted Answer

Secant and sine functions have different signs for angles in the fourth quadrant (where -59° is located). Secant is positive (since it's the reciprocal of cosine, which is positive in the fourth quadrant), and sine is negative in the fourth quadrant.

Question 4

Identify the quadrant for the angle satisfying the following conditions.
-185°52´21´´
A)185.93°
B)185.87°
C)185.83°
D)185.88°

Accepted Answer

185°52´21´´ can be converted to decimal form as follows: 185 + (52/60) + (21/3600) = 185 + 0.8667 + 0.0058 = 185.8725°, which rounds to 185.87°.

Question 5

Provide an appropriate response.
-For what angle $\mathrm { T }$ is $\cos \mathrm { T } \approx 0.866$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$.)
A) $0.866 ^ { \circ }$
B) $28.65 ^ { \circ }$
C) $30 ^ { \circ }$
D) $60 ^ { \circ }$

Accepted Answer

The answer of Provide an appropriate response.
-For what angle \(\mathrm...

Question 6

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
-358°45´12´´
A)358.75°
B)358.71°
C)358.76°
D)358.81°

Accepted Answer

To convert the angle from degrees, minutes, and seconds to decimal degrees, use the formula: Degrees + (Minutes/60) + (Seconds/3600). Thus, 358°45'12'' converts to 358 + (45/60) + (12/3600) = 358 + 0.75 + 0.0033 = 358.7533°, which rounds to 358.75°.

Question 7

Provide an appropriate response.
-For what angle $\mathrm { T }$ is $\sin \mathrm { T } \approx 0.574$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$.)
A) $46.917 ^ { \circ }$
B) $0.574 ^ { \circ }$
C) $55 ^ { \circ }$
D) $35 ^ { \circ }$

Accepted Answer

The answer of Provide an appropriate response.
-For what angle \(\mathrm...

Question 8

Evaluate the expression.
-Find $\cot \theta$, given that $\cos \theta = \frac { 15 } { 17 }$ and $\theta$ is in quadrant IV.
A) $\frac { 17 } { 15 }$
B) $- \frac { 15 \sqrt { 2 } } { 2 }$
C) $- \frac { 15 } { 8 }$
D) $- \frac { 8 } { 15 }$

Accepted Answer

The answer of Evaluate the expression.
-Find $\cot \theta$, given that...

Question 9

Use the fundamental identities to find the value of the trigonometric function.
-Find the complement of an angle whose measure is 33°21´.
A)57°38´
B)57°39´
C)56°39´
D)56°21´

Accepted Answer

The answer of Use the fundamental identities to find the...

Question 10

Use the fundamental identities to find the value of the trigonometric function.
-Find $\tan \theta$, given that $\sec \theta = \frac { 3 } { 2 }$ and $\theta$ is in quadrant IV.
A) $- \sqrt { 5 }$
B) $- \frac { \sqrt { 5 } } { 3 }$
C) $- \frac { 3 } { 2 }$
D) $- \frac { \sqrt { 5 } } { 2 }$

Accepted Answer

The answer of Use the fundamental identities to find the...

Question 11

Solve the problem. Round answers to the nearest tenth if necessary.
-Find the supplement of an angle whose measure is 60°.
A)150°
B)240°
C)120°
D)30°

Accepted Answer

The answer of Solve the problem. Round answers to the...

Question 12

Place your graphing calculator in parametric and degree modes. Set the window for Tmin=0, Tmax=360, Tstep=1, Xmin= $- 1.8 , X _ { \max } = 1.8 , X _ { \text {scl } } = 1 , Y _ { \min } = - 1.2 , Y \max = 1.2 , Y \mathrm { scl } = 1$. Set the functions to $\mathrm { X } _ { 1 \mathrm {~T} } = \cos \mathrm { T } , \mathrm { Y } _ { 1 \mathrm {~T} } = \sin \mathrm { T }$. Graph the circle of radius 1 on the screen. Use the trace feature to move a short distance around the circle.
-90° - 38°21´
A)51°39´
B)52°21´
C)52°39´
D)51°21´

Accepted Answer

To find the difference between 90° and 38°21´, subtract 38°21´ from 90°. This gives 51°39´.

Question 13

Find the angle of least positive measure coterminal with the given angle.
-$\angle \mathrm { Q }$

$\begin{array}{l}
a=56^{\circ} \
b=6 \mathrm{~cm}
\end{array}$

A) $34 ^ { \circ }$
B) $56 ^ { \circ }$
C) $6 \mathrm {~cm}$
D) $90 ^ { \circ }$

Accepted Answer

The answer of Find the angle of least positive measure...

Question 14

The triangles are similar. Find the missing side, angle or value of the variable.
-170° 
A) $530 ^ { \circ }$ and $- 190 ^ { \circ }$

B) $350 ^ { \circ }$ and $- 10 ^ { \circ }$

C) $350 ^ { \circ }$ and $- 10 ^ { \circ }$

D)$530^{\circ} \text { and }-190^{\circ}$

Accepted Answer

The answer of The triangles are similar. Find the missing...

Question 15

Use the properties of angle measures to find the measure of each marked angle.
-65° 
A) $245^{\circ} \text { and }-115^{\circ}$

B) $425^{\circ} \text { and }-295^{\circ}$

C) $245 ^ { \circ }$ and $- 115 ^ { \circ }$

D)$425^{\circ} \text { and }-295^{\circ}$

Accepted Answer

The answer of Use the properties of angle measures to...

Question 16

Find the measure of each angle in the problem.
-cos ϴ, given that sec ϴ = -7 
A) $\frac { 1 } { 7 }$
B) $- \frac { 1 } { 6 }$
C) $\frac { 1 } { 6 }$
D) $- \frac { 1 } { 7 }$

Accepted Answer

The secant of an angle is the reciprocal of the cosine of that angle. Given sec ϴ = -7, the cosine of the angle (cos ϴ) is the reciprocal of -7, which is $- \frac { 1 } { 7 }$.

Question 17

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-
A) $70 ^ { \circ }$ and $20 ^ { \circ }$
B) $35 ^ { \circ }$ and $10 ^ { \circ }$
C) $140 ^ { \circ }$ and $40 ^ { \circ }$
D) $65 ^ { \circ }$ and $35 ^ { \circ }$

Accepted Answer

The answer of Convert the angle to decimal degrees and...

Question 18

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
-Find $\cos \theta$, given that $\tan \theta = - \frac { 8 } { 9 }$ and $\sin \theta > 0$.
A) $- \frac { \sqrt { 145 } } { 9 }$
B) $\frac { 9 \sqrt { 145 } } { 145 }$
C) $\frac { \sqrt { 145 } } { 8 }$
D) $- \frac { 9 \sqrt { 145 } } { 145 }$

Accepted Answer

The answer of Determine the signs of the given trigonometric...

Question 19

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
-(-2, -7)

A)

B)

C)

D)

Accepted Answer

The answer of Draw the given angle in standard position....

Question 20

Use the fundamental identities to find the value of the trigonometric function.
-A triangle drawn on a map has sides of lengths 7 cm, 11 cm, and 15 cm. The shortest of the corresponding real-life distances is 92 km. Find the longest of the real-life distances.
A)207.1 km
B)144.6 km
C)134.6 km
D)197.1 km

Accepted Answer

The answer of Use the fundamental identities to find the...

Quiz 1: Trigonometric Functions

Perform the calculation. - $\cot \theta < 0$ and $\cos \theta > 0$

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. -sec (-59°) and sin (-59°)

Identify the quadrant for the angle satisfying the following conditions. -185°52´21´´

Provide an appropriate response. -For what angle $\mathrm { T }$ is $\cos \mathrm { T } \approx 0.866$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$ .)

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -358°45´12´´

Provide an appropriate response. -For what angle $\mathrm { T }$ is $\sin \mathrm { T } \approx 0.574$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$ .)

Evaluate the expression. -Find $\cot \theta$ , given that $\cos \theta = \frac { 15 } { 17 }$ and $\theta$ is in quadrant IV.

Use the fundamental identities to find the value of the trigonometric function. -Find the complement of an angle whose measure is 33°21´.

Use the fundamental identities to find the value of the trigonometric function. -Find $\tan \theta$ , given that $\sec \theta = \frac { 3 } { 2 }$ and $\theta$ is in quadrant IV.

Solve the problem. Round answers to the nearest tenth if necessary. -Find the supplement of an angle whose measure is 60°.

The triangles are similar. Find the missing side, angle or value of the variable. -170°

Use the properties of angle measures to find the measure of each marked angle. -65°

Find the measure of each angle in the problem. -cos ϴ, given that sec ϴ = -7

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. -Find $\cos \theta$ , given that $\tan \theta = - \frac { 8 } { 9 }$ and $\sin \theta > 0$ .

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -(-2, -7)

Use the fundamental identities to find the value of the trigonometric function. -A triangle drawn on a map has sides of lengths 7 cm, 11 cm, and 15 cm. The shortest of the corresponding real-life distances is 92 km. Find the longest of the real-life distances.

Quiz 1: Trigonometric Functions

Perform the calculation. - cot⁡θ<0\cot \theta < 0cotθ<0 and cos⁡θ>0\cos \theta > 0cosθ>0

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. -sec (-59°) and sin (-59°)

Identify the quadrant for the angle satisfying the following conditions. -185°52´21´´

Provide an appropriate response. -For what angle T\mathrm { T }T is cos⁡T≈0.866\cos \mathrm { T } \approx 0.866cosT≈0.866 ? (Assume 0∘≤T≤90∘0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }0∘≤T≤90∘ .)

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -358°45´12´´

Provide an appropriate response. -For what angle T\mathrm { T }T is sin⁡T≈0.574\sin \mathrm { T } \approx 0.574sinT≈0.574 ? (Assume 0∘≤T≤90∘0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }0∘≤T≤90∘ .)

Evaluate the expression. -Find cot⁡θ\cot \thetacotθ , given that cos⁡θ=1517\cos \theta = \frac { 15 } { 17 }cosθ=1715​ and θ\thetaθ is in quadrant IV.

Use the fundamental identities to find the value of the trigonometric function. -Find the complement of an angle whose measure is 33°21´.

Use the fundamental identities to find the value of the trigonometric function. -Find tan⁡θ\tan \thetatanθ , given that sec⁡θ=32\sec \theta = \frac { 3 } { 2 }secθ=23​ and θ\thetaθ is in quadrant IV.

Solve the problem. Round answers to the nearest tenth if necessary. -Find the supplement of an angle whose measure is 60°.

Find the angle of least positive measure coterminal with the given angle. - ∠Q\angle \mathrm { Q }∠Q a=56∘b=6 cm\begin{array}{l}a=56^{\circ} \\b=6 \mathrm{~cm}\end{array}a=56∘b=6 cm​

The triangles are similar. Find the missing side, angle or value of the variable. -170°

Use the properties of angle measures to find the measure of each marked angle. -65°

Find the measure of each angle in the problem. -cos ϴ, given that sec ϴ = -7

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. -Find cos⁡θ\cos \thetacosθ , given that tan⁡θ=−89\tan \theta = - \frac { 8 } { 9 }tanθ=−98​ and sin⁡θ>0\sin \theta > 0sinθ>0 .

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -(-2, -7)

Use the fundamental identities to find the value of the trigonometric function. -A triangle drawn on a map has sides of lengths 7 cm, 11 cm, and 15 cm. The shortest of the corresponding real-life distances is 92 km. Find the longest of the real-life distances.

Perform the calculation. - $\cot \theta < 0$ and $\cos \theta > 0$

Provide an appropriate response. -For what angle $\mathrm { T }$ is $\cos \mathrm { T } \approx 0.866$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$ .)

Provide an appropriate response. -For what angle $\mathrm { T }$ is $\sin \mathrm { T } \approx 0.574$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$ .)

Evaluate the expression. -Find $\cot \theta$ , given that $\cos \theta = \frac { 15 } { 17 }$ and $\theta$ is in quadrant IV.

Use the fundamental identities to find the value of the trigonometric function. -Find $\tan \theta$ , given that $\sec \theta = \frac { 3 } { 2 }$ and $\theta$ is in quadrant IV.

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. -Find $\cos \theta$ , given that $\tan \theta = - \frac { 8 } { 9 }$ and $\sin \theta > 0$ .