Simplify the trigonometric function

Mathematics

1 answer:

Alisiya [41]3 years ago

8 0

Answer:

a. csc²θ

Step-by-step explanation:

You can use the identities ...

1 +tan² = sec²

cot = cos/sin

sec = 1/cos

csc = 1/sin

___

Then the expression becomes ...

$\cot^2{\theta}(1+\tan^2{\theta})=\cot^2{\theta}\sec^2{\theta}=\dfrac{\cos^2{\theta}}{\sin^2{\theta}\cos^2{\theta}}=\dfrac{1}{\sin^2{\theta}}\\\\=\boxed{\csc^2{\theta}}$

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Three roads, A, B and C, all run south to north. They each meet a highway that runs west to east. Road B is 4.6 mi east of Road

WITCHER [35]

Answer:

Road C is 1.5 mi east of Road A

Step-by-step explanation:

we know that

Road B is 4.6 mi east of Road A

Road C is 3.1 mi west of Road B

Road C is between Road A and Road B

AB=4.6 miles

CB=3.1 miles

AB=AC+CB

Solve for AC

AC=AB-CB

AC=4.6-3.1=1.5 miles

therefore

Road C is 1.5 mi east of Road A

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A giraffe can run 32 miles per hour. What is the speed in feet per second? (1 mile = 5280 ft)

velikii [3]

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