If the opposite side is 7 and the hypotenuse is 25, what is the sine of the angle?

Using the sine definition: $$\text{sine}(\theta) = \frac{7}{25} = 0.28$$ .

If the adjacent side is 12 and the hypotenuse is 13, what is the cosine of the angle?

Using the cosine definition: $$\text{cosine}(\theta) = \frac{12}{13} = 0.923$$ .

If the opposite side is 5 and the adjacent side is 12, what is the tangent of the angle?

Using the tangent definition: $$\text{tangent}(\theta) = \frac{5}{12} = 0.417$$ .

What is the relationship between sine and cosine?

Sine and cosine are related through the identity: $$\text{sine}^2(\theta) + \text{cosine}^2(\theta) = 1$$ .

How do you find the length of a side using sine?

To find a side using sine, rearrange the sine formula: If you know the angle and the hypotenuse, use $$\text{Opposite} = \text{Hypotenuse} \times \text{sine}(\theta)$$ .

How do you find the length of a side using cosine?

To find a side using cosine, rearrange the cosine formula: If you know the angle and the hypotenuse, use $$\text{Adjacent} = \text{Hypotenuse} \times \text{cosine}(\theta)$$ .

What is the significance of the 30-60-90 triangle in trigonometry?

In a 30-60-90 triangle, the sides are in a specific ratio: 1 : $$\frac{\text{\text{sqrt}}{3}}{2}$$ : 2. This makes it easy to calculate side lengths using trigonometric ratios.

SOHCAHTOA Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is SOHCAHTOA?

Back

SOHCAHTOA is a mnemonic used to remember the definitions of the sine, cosine, and tangent functions in a right triangle. It stands for: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

2.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

3.

FLASHCARD QUESTION

Front

How do you find the length of a missing side using the Pythagorean Theorem?

Back

4.

FLASHCARD QUESTION

Front

What is the sine of an angle in a right triangle?

Back

5.

FLASHCARD QUESTION

Front

What is the cosine of an angle in a right triangle?

Back

6.

FLASHCARD QUESTION

Front

What is the tangent of an angle in a right triangle?

Back

7.

FLASHCARD QUESTION

Front

How do you use inverse trigonometric functions?

Back

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