Quiz about Trigonometric Equations And Identities

Question 1

If $$M(t)$$ models the distance (in millions of $${km}$$ ) from Mars to the Sun t days after it's at its furthest point. $$M(t)=21 \cos (\frac{2 \pi}{687} t)+228$$

What does the solution set for $$240=21 \cos (\frac{2 \pi}{687} t)+228$$ ?

Accepted Answer

Covalent bond

Answer

The set of all numbers of days after when Mars is at its furthest point when it is $$240$$ million kilometers from the sun.

Answer

The farthest distance, in millions of kilometers, that Mars reaches from the sun

Answer

The distance, in millions of kilometers, that Mars is from the sun after $$240$$ days

Answer

The least number of days after when Mars is at its furthest point when it is $$240$$ million kilometers from the sun

Question 2

The following are all angle measures (in radians, rounded to the nearest hundredth) whose tangent is $$-1.4$$. Which is the principal value of $$	an ^{-1}(-1.4)$$ ?

Accepted Answer

Covalent bond

Answer

$$-0.95$$

Answer

$$2.19$$

Answer

$$5.33$$

Answer

$$-4.09$$

Question 3

An ice cream truck that plays loud music is circling Bulan's neighborhood. $${C}({t})$$ models the volume of the music (in $${dB}$$ ) that Bulan hears, $${t}$$ minutes after the truck arrives in her neighborhood. Here, $$t$$ is entered in radians.

$$C(t)=-15 \cos (\frac{2 \pi}{15} t)+65$$

How many minutes after the truck arrives does the volume first reach $$75 {~dB}$$ ?

Round your final answer to the nearest tenth of a minute.

Accepted Answer

Covalent bond

Answer

$$5.5$$

Answer

$$7.8$$

Answer

$$4.5$$

Answer

$$6.9$$

Question 4

$$E(t)$$ models the daily amount of energy (in kilojoules, $${kJ}$$ ) that a solar panel in Pago Pago generates, $${t}$$ days after the autumn equinox. Here, $$t$$ is entered in radians.

$${E}({t})=624 \sin (\frac{2 \pi}{365} {t})+8736$$

What is the first day after the autumn equinox that the solar panel generates $$8400 {~kJ}$$ ?

Round your final answer to the nearest whole day.

Accepted Answer

Covalent bond

Answer

$$216$$

Answer

$$332$$

Answer

$$351$$

Answer

$$452$$

Question 5

The following are all angle measures (in degrees, rounded to the nearest tenth) whose tangent is $$-44$$. Which is the principal value of $$	an ^{-1}(-44)$$ ?

Accepted Answer

Covalent bond

Answer

$$-88.7^{\circ}$$

Answer

$$88.7^{\circ}$$

Answer

$$-75.7^{\circ}$$

Answer

$$75.7^{\circ}$$

Trigonometric Equations And Identities Trigonometry Maths Problems and Solutions

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