If cos Z = $$\frac{32}{40}$$ , what is sin Z?

Using the Pythagorean identity: $$\text{sin}^2 Z + \text{cos}^2 Z = 1$$ , we find sin Z = $$\frac{24}{40}$$ .

What is the formula to find the length of the hypotenuse if the opposite side is 5 and the angle is 30 degrees?

$$\text{hypotenuse} = \frac{5}{\text{sin}(30^\text{degree})} = 10$$ .

What is the relationship between sine and cosine for complementary angles?

$$\text{sin}(90^\text{degree} - \theta) = \text{cos}(\theta)$$ .

If sin 56° = $$\frac{x}{20}$$ , how do you solve for x?

Multiply both sides by 20: $$x = 20 \times \text{sin}(56^\text{degree})$$ .

What is the definition of the adjacent side in relation to an angle in a right triangle?

The adjacent side is the side next to the angle that is not the hypotenuse.

How do you identify the hypotenuse in a right triangle?

The hypotenuse is the longest side of the triangle, opposite the right angle.

What is the cosine ratio for angle X if the adjacent side is 12 and the hypotenuse is 13?

$$\text{cos} X = \frac{12}{13}$$ .

If tan Z = $$\frac{12}{5}$$ , what are the lengths of the opposite and adjacent sides?

Opposite side = 12, Adjacent side = 5.

What is the sine of an angle if the opposite side is 20 and the hypotenuse is 25?

$$\text{sin} = \frac{20}{25} = \frac{4}{5}$$ .

Intro to Trigonometry Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the definition of cosine in a right triangle?

Back

Cosine (cos) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

2.

FLASHCARD QUESTION

Front

What is the definition of sine in a right triangle?

Back

Sine (sin) of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

3.

FLASHCARD QUESTION

Front

What is the definition of tangent in a right triangle?

Back

Tangent (tan) of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

4.

FLASHCARD QUESTION

Front

What is the Pythagorean theorem?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the sine ratio for angle Z if the opposite side is 5 and the hypotenuse is 13?

Back

7.

FLASHCARD QUESTION

Front

Which trigonometric function is used when given the opposite and adjacent sides?

Back

Tangent.

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