How do you find coterminal angles for $$eta = 95^{\text{°}}$$ ?

To find coterminal angles, add or subtract 360°: 1. $$95^{\text{°}} + 360^{\text{°}} = 455^{\text{°}}$$ 2. $$95^{\text{°}} - 360^{\text{°}} = -265^{\text{°}}$$ Thus, coterminal angles are $$455^{\text{°}}$$ and $$-265^{\text{°}}$$ .

What is the value of $$\tan\frac{5\text{π}}{6}$$ ?

The value of $$\tan\frac{5\text{π}}{6}$$ is $$-\frac{\text{√}3}{3}$$ .

How do you solve the equation $$2\text{sin}^2x - \text{sin}x - 1 = 0$$ ?

This is a quadratic equation in terms of $$\text{sin}x$$ . Factor or use the quadratic formula to find solutions. The solutions in the interval $$[0, 2\text{π})$$ are $$x = \frac{7\text{π}}{6}, \frac{11\text{π}}{6}, \frac{\text{π}}{2}$$ .

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

For complementary angles, the sine of one angle is equal to the cosine of the other: $$\text{sin}(\theta) = \text{cos}(90^{\text{°}} - \theta)$$ .

How do you convert degrees to radians?

To convert degrees to radians, multiply by $$\frac{\text{π}}{180}$$ . For example, $$180^{\text{°}} = 180 \times \frac{\text{π}}{180} = \text{π}$$ .

What is the unit circle?

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. It is used to define trigonometric functions for all angles.

What is the value of $$\text{sin}(0)$$ ?

The value of $$\text{sin}(0)$$ is 0.

What is the value of $$\text{cos}(90^{\text{°}})$$ ?

The value of $$\text{cos}(90^{\text{°}})$$ is 0.

What is the Pythagorean identity involving sine and cosine?

The Pythagorean identity states that $$\text{sin}^2(x) + \text{cos}^2(x) = 1$$ for any angle x.

How do you find the reference angle for an angle in the second quadrant?

To find the reference angle for an angle in the second quadrant, subtract the angle from 180°: Reference angle = $$180^{\text{°}} - \theta$$ .

What is the value of $$\tan(45^{\text{°}})$$ ?

The value of $$\tan(45^{\text{°}})$$ is 1.

Part 2 Semester Final 24-25 Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Define coterminal angles.

Back

Coterminal angles are angles that share the same terminal side when drawn in standard position. They can be found by adding or subtracting multiples of 360° (or 2π radians) to/from the angle.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the sine of an angle greater than 360°?

Back

6.

FLASHCARD QUESTION

Front

Define the sine function in terms of a right triangle.

Back

7.

FLASHCARD QUESTION

Front

What is the range of the sine function?

Back

The range of the sine function is from -1 to 1, inclusive.

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