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3 years ago

Find csc theta and sin theta if tan theta = 7/4 and sin theta less than 0

Mathematics

1 answer:

stiv31 [10]3 years ago

8 0

9514 1404 393

Answer:

sin(θ) = (-7√65)/65

csc(θ) = (-√65)/7

Step-by-step explanation:

The angle will have the given characteristics if its terminal ray passes through the 3rd-quadrant point (-4, -7). The distance from the origin to that point is ...

d = √((-4)² +(-7)²) = √65

The sine of the angle is the ratio of the y-coordinate to this value:

sin(θ) = -7/√65

sin(θ) = (-7√65)/65

The cosecant is the inverse of the sine

csc(θ) = (-√65)/7

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Step-by-step explanation:

Just simplify each the statements.

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Step-by-step explanation:

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3 years ago

Express sin A,cos A and tan A as ratios

OverLord2011 [107]

Answer:

Part A) $sin(A)=\frac{2\sqrt{42}}{23}$

Part B) $cos(A)=\frac{19}{23}$

Part C) $tan(A)=\frac{2\sqrt{42}}{19}$

Step-by-step explanation:

Part A) we know that

In the right triangle ABC of the figure the sine of angle A is equal to divide the opposite side angle A by the hypotenuse

$sin(A)=\frac{BC}{AB}$

substitute the values

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Part B) we know that

In the right triangle ABC of the figure the cosine of angle A is equal to divide the adjacent side angle A by the hypotenuse

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substitute the values

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Part C) we know that

In the right triangle ABC of the figure the tangent of angle A is equal to divide the opposite side angle A by the adjacent side angle A

$tan(A)=\frac{BC}{AC}$

substitute the values

$tan(A)=\frac{2\sqrt{42}}{19}$

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givi [52]

Answer:

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