What is the length of the hypotenuse if the opposite side is 30 and the adjacent side is 40?

Using the Pythagorean theorem: $$c = \text{hypotenuse} = \text{sqrt}(30^2 + 40^2) = 50$$ .

What is the length of the side opposite ∠Z if the hypotenuse is 34 and the sine of ∠Z is 0.8824?

The length of the side opposite ∠Z is calculated as: $$\text{opposite} = \text{sine} \times \text{hypotenuse} = 0.8824 \times 34 = 30$$ .

What is the length of the side adjacent to ∠X if the hypotenuse is 25 and the cosine of ∠X is 0.96?

The length of the side adjacent to ∠X is calculated as: $$\text{adjacent} = \text{cosine} \times \text{hypotenuse} = 0.96 \times 25 = 24$$ .

What is the relationship between sine, cosine, and tangent?

The relationship is given by: $$\tan(\theta) = \frac{\text{sine}(\theta)}{\text{cosine}(\theta)}$$ .

If the angle is 30 degrees, what is the sine value?

The sine value for 30 degrees is $$\frac{1}{2}$$ .

If the angle is 45 degrees, what is the cosine value?

The cosine value for 45 degrees is $$\frac{\text{sqrt}(2)}{2}$$ .

What is the sine of an angle in terms of the unit circle?

In the unit circle, the sine of an angle is the y-coordinate of the point where the terminal side of the angle intersects the circle.

What is the cosine of an angle in terms of the unit circle?

In the unit circle, the cosine of an angle is the x-coordinate of the point where the terminal side of the angle intersects the circle.

Trigonometric Ratios and Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the sine ratio in a right triangle?

Back

2.

FLASHCARD QUESTION

Front

What is the cosine ratio in a right triangle?

Back

3.

FLASHCARD QUESTION

Front

What is the tangent ratio in a right triangle?

Back

4.

FLASHCARD QUESTION

Front

If the opposite side is 30 and the hypotenuse is 34, what is the sine of the angle?

Back

5.

FLASHCARD QUESTION

Front

If the adjacent side is 24 and the hypotenuse is 25, what is the cosine of the angle?

Back

6.

FLASHCARD QUESTION

Front

If the opposite side is 30 and the adjacent side is 40, what is the tangent of the angle?

Back

7.

FLASHCARD QUESTION

Front

What is the Pythagorean theorem?

Back

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