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pickupchik [31]
3 years ago
11

Find the exact values of a) sec of theta b)tan of theta if cos of theta= -4/5 and sin<0

Mathematics
1 answer:
Gre4nikov [31]3 years ago
7 0

Answer:

Using trigonometric ratio:

\sec \theta = \frac{1}{\cos \theta}

\tan \theta = \frac{\sin \theta}{\cos \theta}

From the given statement:

\cos \theta = -\frac{4}{5} and sin < 0

⇒\theta lies in the 3rd quadrant.

then;

\sec \theta = \frac{1}{-\frac{4}{5}} = -\frac{5}{4}

Using trigonometry identities:

\sin \theta = \pm \sqrt{1-\cos^2 \theta}

Substitute the given values we have;

\sin \theta = \pm\sqrt{1-(\frac{-4}{5})^2 } =\pm\sqrt{1-\frac{16}{25}} =\pm\sqrt{\frac{25-16}{25}} =\pm \sqrt{\frac{9}{25} } = \pm\frac{3}{5}

Since, sin < 0

⇒\sin \theta = -\frac{3}{5}

now, find \tan \theta:

\tan \theta = \frac{\sin \theta}{\cos \theta}

Substitute the given values we have;

\tan \theta = \frac{-\frac{3}{5} }{-\frac{4}{5} } = \frac{3}{5}\times \frac{5}{4} = \frac{3}{4}

Therefore, the exact value of:

(a)

\sec \theta =-\frac{5}{4}

(b)

\tan \theta= \frac{3}{4}

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Answer:

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Step-by-step explanation:

Given

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6 0
3 years ago
A plane flew for 5 hours heading west and for 4 hours heading south. If the total distance traveled was 3,444 miles, and the pla
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Answer:400 miles per hour

Step-by-step explanation:

Let w = speed at which the plane travelled west

Let s = speed at which the plane travelled south

Distance moved in 5 hrs heading west = 5*w = 5w

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Total distance, 3444= 5w + 4s

w = s + 39( 39 miles/hr faster)

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3 years ago
50 POINTS!!
Andre45 [30]

Answer:Triangle A: 38 degrees

Triangle B: Unknown (not enough information)

Triangle C: Unknown (not enough information)

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Step-by-step explanation:

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3 years ago
Read 2 more answers
Carrie has 40 more nickels than Joan has dimes. They both have the same amount of money. How many coins does each girl have? Wha
LuckyWell [14K]

Answer:

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

Step-by-step explanation:

Let be x and y the amounts of nickels and dimes that Carrie and Joan have, as c the total amount of money that both Carrie and Joan have. A nickel is a five cent coin and a dime is a ten cent coin.

The following equations are constructed after a careful reading on statement:

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First we eliminate c by equalizing (Eq. 1) and (Eq. 2):

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c = 0.05\cdot (80)

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Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

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