Question 1

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined.
(a)
 $\cos ^ { - 1 } ( - 3 / 4 )$ 
(b)
 $\sin ^ { - 1 } ( 0.25 )$

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Question 2

Find the area of the shaded region.

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Question 3

Find the values of the trigonometric functions of $\theta$ given that $\cot \theta = - \frac { 4 } { 3 }$ and $\text { sect } > 0$ .

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Question 4

Find the quadrant in which $\theta$ lies given that $\cot \theta > 0$ and $\sin \theta < 0$ .

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Question 5

Find the exact value of $\cot \left( - 675 ^ { \circ } \right)$ .

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Question 6

The time in seconds that it takes for a sled to slide down a hillside inclined at an angle $\theta$ is $t = \sqrt { \frac { d } { 16 \sin \theta } }$ where d is the length of the slope in feet. Find the time it takes to slide down a 4000-ft slope inclined at $30 ^ { \circ }$

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Question 7

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined.
(a)
 $\tan ^ { - 1 } ( 3 )$ 
(b)
 $\sin ^ { - 1 } ( - 3 )$

Accepted Answer

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Question 8

Find the exact value of $\csc ( - \pi / 3 )$ .

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Question 9

Find the area of the shaded region.

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Question 10

Find the exact value of each expression, if it is defined.
(a) $\cos ^ { - 1 } ( - 1 )$
(b) $\sin ^ { - 1 } ( - 1 )$
(c) $\tan ^ { - 1 } ( - 1 )$

Accepted Answer

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Question 11

Find the exact value of each expression, if it is defined.
(a) $\cos ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$
(b) $\sin ^ { - 1 } \left( - \frac { 1 } { 2 } \right)$
(c) $\tan ^ { - 1 } ( - 1 )$

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Question 12

Find the exact value of $\sin ( 19 \pi / 2 )$ .

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Question 13

Find the exact value of each expression, if it is defined.
(a) $\cos ^ { - 1 } ( - \sqrt { 2 } / 2 )$
(b) $\sin ^ { - 1 } ( - \sqrt { 2 } / 2 )$
(c) $\tan ^ { - 1 } ( - \sqrt { 3 } )$

Accepted Answer

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Question 14

Find the area of a triangle with sides of length 12 and 22 and included angle $12 ^ { \circ }$ .

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Question 15

Find the exact value of each expression, if it is defined.
(a) $\cos ^ { - 1 } \left( - \frac { 1 } { 2 } \right)$
(b) $\sin ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 2 } \right)$
(c) $\tan ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 3 } \right)$

Accepted Answer

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Question 16

Find the values of the trigonometric functions of $\theta$ given that $\sec \theta = - 2$ and $\tan \theta > 0$ .

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Question 17

The time in seconds that it takes for a sled to slide down a hillside inclined at an angle $\theta$ is $t = \sqrt { \frac { d } { 16 \sin \theta } }$ where d is the length of the slope in feet. Find the time it takes to slide down a 5000-ft slope inclined at $30 ^ { \circ }$

Accepted Answer

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Question 18

Find the area of the triangle.

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Question 19

Find the exact value of $\csc ( - 23 \pi / 4 )$ .

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Question 20

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined.
(a)
 $\cos ^ { - 1 } ( - 0.25 )$ 
(b)
 $\sin ^ { - 1 } ( 3 / 4 )$

Accepted Answer

The answer of Use a calculator to find an approximate...

Quiz 6: Trigonometric Functions: Right Triangle Approach

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. (a) cos⁡−1(−3/4)\cos ^ { - 1 } ( - 3 / 4 )cos−1(−3/4) (b) sin⁡−1(0.25)\sin ^ { - 1 } ( 0.25 )sin−1(0.25)

Find the area of the shaded region.

Find the values of the trigonometric functions of θ\thetaθ given that cot⁡θ=−43\cot \theta = - \frac { 4 } { 3 }cotθ=−34​ and sect >0\text { sect } > 0 sect >0 .

Find the quadrant in which θ\thetaθ lies given that cot⁡θ>0\cot \theta > 0cotθ>0 and sin⁡θ<0\sin \theta < 0sinθ<0 .

Find the exact value of cot⁡(−675∘)\cot \left( - 675 ^ { \circ } \right)cot(−675∘) .

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. (a) tan⁡−1(3)\tan ^ { - 1 } ( 3 )tan−1(3) (b) sin⁡−1(−3)\sin ^ { - 1 } ( - 3 )sin−1(−3)

Find the exact value of csc⁡(−π/3)\csc ( - \pi / 3 )csc(−π/3) .

Find the area of the shaded region.

Find the exact value of each expression, if it is defined. (a) cos⁡−1(−1)\cos ^ { - 1 } ( - 1 )cos−1(−1) (b) sin⁡−1(−1)\sin ^ { - 1 } ( - 1 )sin−1(−1) (c) tan⁡−1(−1)\tan ^ { - 1 } ( - 1 )tan−1(−1)

Find the exact value of each expression, if it is defined. (a) cos⁡−1(32)\cos ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)cos−1(23​​) (b) sin⁡−1(−12)\sin ^ { - 1 } \left( - \frac { 1 } { 2 } \right)sin−1(−21​) (c) tan⁡−1(−1)\tan ^ { - 1 } ( - 1 )tan−1(−1)

Find the exact value of sin⁡(19π/2)\sin ( 19 \pi / 2 )sin(19π/2) .

Find the exact value of each expression, if it is defined. (a) cos⁡−1(−2/2)\cos ^ { - 1 } ( - \sqrt { 2 } / 2 )cos−1(−2​/2) (b) sin⁡−1(−2/2)\sin ^ { - 1 } ( - \sqrt { 2 } / 2 )sin−1(−2​/2) (c) tan⁡−1(−3)\tan ^ { - 1 } ( - \sqrt { 3 } )tan−1(−3​)

Find the area of a triangle with sides of length 12 and 22 and included angle 12∘12 ^ { \circ }12∘ .

Find the values of the trigonometric functions of θ\thetaθ given that sec⁡θ=−2\sec \theta = - 2secθ=−2 and tan⁡θ>0\tan \theta > 0tanθ>0 .

Find the area of the triangle.

Find the exact value of csc⁡(−23π/4)\csc ( - 23 \pi / 4 )csc(−23π/4) .

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. (a) cos⁡−1(−0.25)\cos ^ { - 1 } ( - 0.25 )cos−1(−0.25) (b) sin⁡−1(3/4)\sin ^ { - 1 } ( 3 / 4 )sin−1(3/4)

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. (a) $\cos ^ { - 1 } ( - 3 / 4 )$ (b) $\sin ^ { - 1 } ( 0.25 )$

Find the values of the trigonometric functions of $\theta$ given that $\cot \theta = - \frac { 4 } { 3 }$ and $\text { sect } > 0$ .

Find the quadrant in which $\theta$ lies given that $\cot \theta > 0$ and $\sin \theta < 0$ .

Find the exact value of $\cot \left( - 675 ^ { \circ } \right)$ .

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. (a) $\tan ^ { - 1 } ( 3 )$ (b) $\sin ^ { - 1 } ( - 3 )$

Find the exact value of $\csc ( - \pi / 3 )$ .

Find the exact value of each expression, if it is defined. (a) $\cos ^ { - 1 } ( - 1 )$ (b) $\sin ^ { - 1 } ( - 1 )$ (c) $\tan ^ { - 1 } ( - 1 )$

Find the exact value of each expression, if it is defined. (a) $\cos ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$ (b) $\sin ^ { - 1 } \left( - \frac { 1 } { 2 } \right)$ (c) $\tan ^ { - 1 } ( - 1 )$

Find the exact value of $\sin ( 19 \pi / 2 )$ .

Find the exact value of each expression, if it is defined. (a) $\cos ^ { - 1 } ( - \sqrt { 2 } / 2 )$ (b) $\sin ^ { - 1 } ( - \sqrt { 2 } / 2 )$ (c) $\tan ^ { - 1 } ( - \sqrt { 3 } )$

Find the area of a triangle with sides of length 12 and 22 and included angle $12 ^ { \circ }$ .

Find the values of the trigonometric functions of $\theta$ given that $\sec \theta = - 2$ and $\tan \theta > 0$ .

Find the exact value of $\csc ( - 23 \pi / 4 )$ .

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. (a) $\cos ^ { - 1 } ( - 0.25 )$ (b) $\sin ^ { - 1 } ( 3 / 4 )$